The number of solutions of $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is.

The set of values of $x$ for which the expression $\frac{{\tan 3x - \tan 2x}}{{1 + \tan 3x\tan 2x}} = 1$, is

The sum of solutions of the equation $\frac{\cos \mathrm{x}}{1+\sin \mathrm{x}}=|\tan 2 \mathrm{x}|, \mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\left\{\frac{\pi}{4},-\frac{\pi}{4}\right\}$ is :

Let $S$ be the sum of all solutions (in radians) of the equation $\sin ^{4} \theta+\cos ^{4} \theta-\sin \theta \cos \theta=0$ in $[0,4 \pi]$ Then $\frac{8 \mathrm{~S}}{\pi}$ is equal to ...... .

The number of integral values of $k$, for which the equation $7\cos x + 5\sin x = 2k + 1$ has a solution, is

If $\frac{{1 - {{\tan }^2}\theta }}{{{{\sec }^2}\theta }} = \frac{1}{2}$, then the general value of $\theta $ is