Method 3 (my favourite):
sin(2x) = -sin(3x) = sin(-3x).
Therefore (working in degrees):
Case 1:
2x = -3x + 360n, n is an integer
=> 5x = 360n
=> x = 72n
=> x = 0, 72, 144, 216, 288 (assuming 0 < x < 360).
Case 2:
2x = 180 - (-3x) + 360n, n is an integer
=> -x = 180 + 360n = 180(1 + 2n)
=> x = -180(2n + 1)
=> x = 180 (assuming 0 < x< 360).