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

   Start from the equation as given.

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

   Bring everything to one side.

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

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

4. \left\{2 n \pi + \frac{\pi}{6}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + \frac{5 \pi}{6}\; \middle|\; n \in \mathbb{Z}\right\}

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

5. x = \frac{\pi}{6} \approx 0.52360 ,\; x = \frac{5 \pi}{6} \approx 2.6180

   Solve for the variable.