Therefore, I will only show the general direction for you to solve, leaving the final and detailed implementation to you.
From sin(x+y) = = , it follows that
x + y = 45° OR x + y = 135°.
From cos(2x) = - , it follows that
2x = 120° OR 2x = 240°, i.e.
x = 60° OR x = 120°.
Therefore, you need to solve 4 (four) systems of equations
1) x + y = 45 (mod 360)
x = 60 (mod 360)
2) x + y = 135 (mod 360)
x = 60 (mod 360)
3) x + y = 45 (mod 360)
x = 120 (mod 360)
4) x + y = 135 (mod 360)
x = 120 (mod 360)
Solution of each and every system 1) to 4) is an elementary task.
The solution to the original problem will be the union of the solutions of partial problems 1) - 4).
