Plotting f(x,y,z)=0?

[roadrunner]

Maybe you can use fsolve to solve for z like this:

p:=(x,y,n)->(fsolve((cos(x)*sin(y)+cos(y)*sin(z)+cos(z)*sin(x)) = 0,z,0 .. (2*π)))(n)

That give 2 solutions between 0 and 2*pi so you can plot each one separately:

FZ1(X,Y)=p(X,Y,1) and FZ2((X,Y)=p(X,Y,2)

-road