Find the principal solutions of the equation $\tan x = -\frac{1}{\sqrt{3}}.$

The general solution of the trigonometric equation $(\sqrt{3}-1) \sin \theta + (\sqrt{3}+1) \cos \theta = 2$ is

The general solution of the equation $\sqrt{3-5 \sin x+\sin ^2 x}+\cos x=0$ is

The solution set of the equation $\cos^2 2x + \sin^2 3x = 1$ is

If $\sin \theta + \cos \theta = \sqrt{2} \cos \alpha$,then the general value of $\theta$ is

If the sum of all the solutions of the equation $8 \cos x \cdot \left( \cos \left( \frac{\pi}{6} + x \right) \cdot \cos \left( \frac{\pi}{6} - x \right) - \frac{1}{2} \right) = 1$ in the interval $[0, \pi]$ is $k\pi$,then $k$ is equal to: