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1. \sin{\left(2 x \right)} = \frac{1}{2}

   Start from the equation as given.

2. \sin{\left(2 x \right)} - \frac{1}{2} = 0

   Bring everything to one side.

3. \sin{\left(2 x \right)} - \frac{1}{2} = 0

   Isolate the trig function, then read the reference angle off the unit circle. Solutions repeat every period.

4. \left\{n \pi + \frac{\pi}{12}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{n \pi + \frac{5 \pi}{12}\; \middle|\; n \in \mathbb{Z}\right\}

   General solution over the reals (n is any integer).

5. x = \frac{\pi}{12} \approx 0.26180 ,\; x = \frac{5 \pi}{12} \approx 1.3090

   Solve for the variable.