The number of values of $\theta $ in $[0, 2\pi]$ satisfying the equation $2{\sin ^2}\theta = 4 + 3$$\cos \theta $ are

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) -

For $n \in Z$ , the general solution of the equation

$(\sqrt 3  - 1)\,\sin \,\theta \, + \,(\sqrt 3  + 1)\,\cos \theta \, = \,2$ is

The number of solutions of $tan\, (5\pi\, cos\, \theta ) = cot (5 \pi \,sin\, \theta )$ for $\theta$ in $(0, 2\pi )$ is :

If $\cos \theta + \cos 7\theta + \cos 3\theta + \cos 5\theta = 0$, then $\theta $

If $2\sin \theta + \tan \theta = 0$, then the general values of $\theta $ are