how to find all possible stationary points of a system of nonlinear equations

I stumbled across this seemingly simple problem:

I tried using fsolve, but I can only pass in a single initial guess. Is there a smart way to do this?

Answer 1

[Torsten]

Your equation could become stationary if

2*x + y = pi/2 or pi + pi/2 or 2*pi+pi/2 or ... or 6*pi+pi/2

3*x + 2*y = pi/3 or pi+pi/3 or 2*pi+pi/3 or ... or 10*pi+pi/3

So solve the 7*11 possible linear systems and select those solutions for x and y for which 0<=x<=2*pi, 0<=y<=2*pi.

I get 4 solutions.