Find all solutions in the interval [0,2pi].

Question

sin 2x + sin x = 0

Answer 1

sin 2 x = 2 sin x cos x

2 sin x cos x + sin x = 0

sin x (2 cos x + 1) = 0
so
x = 0 is a solution and x = 180 is a solution
then
cos x = -1/2
that is at x = 120 and x = 240

Answer 2

We should also include 360° , (from sinx = 0)