Verified answer

You can simply restate the problem without the multiple angle and figure out the solution---of course this must be done properly.

Let Θ = 2x.

Then the problem reduces to: solve

sinΘ = 1/2.

But, be careful, if 0 ≤ x < 2π, this will mean (multply through by 2)

0 ≤ 2x < 4π ----that is 0 ≤ Θ < 4π.

There are four such Θs on the interval [0, 4π) (two for each full revolution)

Θ = π/6, 5π/6, 13π/6, and 17π/6.

Going back to x, just use that x = ½Θ. So the solutions x are

x = π/12, 5π/12, 13π/12, and 17π/12.

(Note that they are all between 0 and 2π as they were required to be.)