The number of distinct solutions of the equation $\log _{\frac{1}{2}}|\sin x|=2-\log _{\frac{1}{2}}|\cos x|$ in the interval $[0,2 \pi],$ is

Values of $\theta (0 < \theta < {360^o})$ satisfying ${\rm{cosec}}\theta + 2 = 0$ are

The number of real solutions of the equation $2 \sin 3 x+\sin 7 x-3=0$, which lie in the interval $[-2 \pi, 2 \pi]$ is

Number of solutions of equation $sgn(sin x) = sin^2x + 2sinx + sgn(sin^2x)$ in $\left[ { - \frac{{5\pi }}{2},\frac{{7\pi }}{2}} \right]$  is

(where $sgn(.)$ denotes signum function) -

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 :

If $\sqrt 3 \tan 2\theta + \sqrt 3 \tan 3\theta + \tan 2\theta \tan 3\theta = 1$, then the general value of $\theta $ is