2. $$Sin(\frac{x}{2} - \frac{\pi}{6}) + 1 = 0$$

Решим уравнение:

$$Sin(\frac{x}{2} - \frac{\pi}{6}) + 1 = 0$$

$$Sin(\frac{x}{2} - \frac{\pi}{6}) = -1$$

$$\frac{x}{2} - \frac{\pi}{6} = arcsin(-1) + 2\pi k, k \in Z$$

$$\frac{x}{2} - \frac{\pi}{6} = -\frac{\pi}{2} + 2\pi k, k \in Z$$

$$\frac{x}{2} = -\frac{\pi}{2} + \frac{\pi}{6} + 2\pi k, k \in Z$$

$$\frac{x}{2} = -\frac{3\pi}{6} + \frac{\pi}{6} + 2\pi k, k \in Z$$

$$\frac{x}{2} = -\frac{2\pi}{6} + 2\pi k, k \in Z$$

$$\frac{x}{2} = -\frac{\pi}{3} + 2\pi k, k \in Z$$

$$x = -\frac{2\pi}{3} + 4\pi k, k \in Z$$

Ответ: $$x = -\frac{2\pi}{3} + 4\pi k, k \in Z$$