The following sequence of commands does the job:
trigreduce(2*cos(x)^2*x0+2*sin(x)*cos(x)*y0-x0)=0;
subst(z,2*x,%);
expand(%);
%/cos(z);
expand(%);
trigreduce(%);
subst(2*x,z,%);
solve(%,x);
But I'm afraid that future generations growing up with CAS programs and
poor mathematical knowledge (for instance, Danish students no more learn
about trigonometric addition formulae) will never find a solution... - or
maybe even worse: They will believe that the equation is not solvable!
BTW, I was rather astonished to see that Maxima could not even solve the
simple trigonometric equation y0*sin(z) + x0* cos(z)=0 automatically
byjust typing
solve(y0*sin(z) + x0* cos(z)=0,z);
Poul Riis