The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is
$\theta = n\pi + \frac{\pi }{2} - \alpha $
$\theta = n\pi - \frac{\pi }{2} + \alpha $
$\theta = n\pi + \frac{\pi }{2} + \alpha $
$\theta = n\pi - \frac{\pi }{2} - \alpha $
Let $\theta \in [0, 4\pi ]$ satisfy the equation $(sin\, \theta + 2) (sin\, \theta + 3) (sin\, \theta + 4) = 6$ . If the sum of all the values of $\theta $ is of the form $k\pi $, then the value of $k$ is
The general value of $\theta $satisfying the equation $2{\sin ^2}\theta - 3\sin \theta - 2 = 0$ is
The values of $\theta $ satisfying $\sin 7\theta = \sin 4\theta - \sin \theta $ and $0 < \theta < \frac{\pi }{2}$ are
Find the principal solutions of the equation $\tan x=-\frac{1}{\sqrt{3}}.$
The number of solutions of $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is.