F.4 trigonometry---

sin3x + cos3x = sinx + cosx

sin 3x - sin x = cos x - cos 3x

2 sin x cos 2x = 2 sin 2x sin x

sin x (sin 2x - cos 2x) = 0

sin x = 0 or tan 2x = 1

x = 0, π or 2x = π/4, 5π/4

x = 0, π, π/8 or 5π/8