Find all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π. (enter your answers as a comma-separated list.)

Hello:

sin 2x = sin x and 0 ≤ x ≤ 2π ... 51°

note : sina = sinb equivaut : (a = b + 2k π) or (a = π - b + 2kπ) ... k∈ Z

(1) equiv : (2x = x + 2kπ) or (2x = π - x + 2kπ)

(x = 2kπ) or (x = π/3 + 2kπ/3) ... (general solution)

but : 0 ≤ x ≤ 2π

k = 0 : x = 0, x = π/3

k = 1 : x = 2π, x = π

k = 2; x = 5π/3