Find the exact solutions of sin (2x) - sin (x) = 0 in the interval [0, 2pi)

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

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

sin (x) * (2cos (x) - 1) = 0

Sin (x) = 0 = > x [PiK]

Cos (x) = 1/2 = > x[Pi/3 + (2PiK/3)

K=0 x=0

K=1 x=Pi

K=2 x=5Pi/3

So the answer is 0, Pi, 5Pi/3