Find the general solution: sinx + sin3x + sin5x = 0

sinx + sin3x + sin5x = 0
→ sinx + sin5x + sin3x = 0
→ 2sin(x+5x/2)cos(5x-x/2) + sin3x = 0
→ 2sin(3x)cos(2x) + sin3x = 0
→ sin3x(2cos2x + 1) = 0
→ sin3x = 0 or cos2x = -1/2
→ 3x = nπ or 2x = 2nπ ± π/3
→ x = nπ/3, nπ ± π/6