101.sagews

x,y,z = var('x y z');
a=matrix(3,[cos(x),-sin(x),0,sin(x),cos(x),0,0,0,1]);
b=matrix(3,[cos(y)*cos(z),-sin(z),sin(y)*cos(z),cos(y)*sin(z),cos(z),sin(y)*sin(z),-sin(y),0,cos(y)]);
c=b.inverse();
d=b*a*c;
d*(d.transpose());

[ ((cos(x)*cos(y)*cos(z) - sin(x)*sin(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*cos(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))^2 + ((-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))^2 + (cos(y)*sin(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))^2 ((cos(x)*cos(y)*cos(z) - sin(x)*sin(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*cos(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(y)*sin(z) + sin(x)*cos(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*sin(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (cos(y)*sin(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*(sin(y)^2*sin(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(cos(x)*cos(z) - sin(x)*cos(y)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + ((-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(z) - sin(x)*cos(y)*sin(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) (cos(y)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*sin(y)*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(y)*cos(z) - sin(x)*sin(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*cos(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (sin(x)*sin(y)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (-cos(x)*cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(x)*sin(y)*(sin(y)^2*cos(z) + cos(y)^2*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*(cos(y)*sin(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))] [((cos(x)*cos(y)*cos(z) - sin(x)*sin(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*cos(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(y)*sin(z) + sin(x)*cos(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*sin(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (cos(y)*sin(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*(sin(y)^2*sin(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(cos(x)*cos(z) - sin(x)*cos(y)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + ((-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(z) - sin(x)*cos(y)*sin(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) ((cos(x)*cos(y)*sin(z) + sin(x)*cos(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*sin(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))^2 + (sin(y)^2*sin(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(cos(x)*cos(z) - sin(x)*cos(y)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))^2 + ((cos(x)*cos(z) - sin(x)*cos(y)*sin(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))^2 (cos(y)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*sin(y)*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(y)*sin(z) + sin(x)*cos(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*sin(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (-cos(x)*cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(x)*sin(y)*(sin(y)^2*cos(z) + cos(y)^2*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*(sin(y)^2*sin(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(cos(x)*cos(z) - sin(x)*cos(y)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (sin(x)*sin(y)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(z) - sin(x)*cos(y)*sin(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))] [ (cos(y)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*sin(y)*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(y)*cos(z) - sin(x)*sin(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*cos(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (sin(x)*sin(y)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (-cos(x)*cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(x)*sin(y)*(sin(y)^2*cos(z) + cos(y)^2*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*(cos(y)*sin(z)*(cos(x)*cos(y)*cos(z) - sin(x)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(-cos(x)*sin(z) - sin(x)*cos(y)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) (cos(y)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*sin(y)*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(y)*sin(z) + sin(x)*cos(z))*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)*sin(z)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (-cos(x)*cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(x)*sin(y)*(sin(y)^2*cos(z) + cos(y)^2*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*(sin(y)^2*sin(z)^2/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + (sin(y)^2*cos(z) + cos(y)^2*cos(z))*(cos(x)*cos(z) - sin(x)*cos(y)*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) + (sin(x)*sin(y)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))*((cos(x)*cos(z) - sin(x)*cos(y)*sin(z))*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*cos(z)*(cos(x)*cos(y)*sin(z) + sin(x)*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(y)^2*cos(z)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2)) (cos(y)*(cos(y)*sin(z)^2 + cos(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*sin(y)*(-sin(y)*sin(z)^2 - sin(y)*cos(z)^2)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))^2 + (sin(x)*sin(y)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) - cos(x)*cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*cos(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))^2 + (-cos(x)*cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + cos(y)*sin(y)*sin(z)/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2) + sin(x)*sin(y)*(sin(y)^2*cos(z) + cos(y)^2*cos(z))/(-sin(z)*(-sin(y)^2*sin(z) - cos(y)^2*sin(z)) + sin(y)^2*cos(z)^2 + cos(y)^2*cos(z)^2))^2]