Let $P = \left\{ {\theta :\sin \,\theta  - \cos \,\theta  = \sqrt 2 \,\cos \,\theta } \right\}$ and $Q = \left\{ {\theta :\sin \,\theta  + \cos \,\theta  = \sqrt {2\,} \sin \,\theta } \right\}$ be two sets. Then

For which value of $x$  ;  $cosx > sinx,$ where $x\, \in \,\,\left( {\frac{\pi }{2}\,,\,\frac{{3\pi }}{2}} \right)$

If $\cos \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1$, then the general value of $\theta $ is

The positive integer value of $n>3$ satisfying the equation $\frac{1}{\sin \left(\frac{\pi}{n}\right)}=\frac{1}{\sin \left(\frac{2 \pi}{n}\right)}+\frac{1}{\sin \left(\frac{3 \pi}{n}\right)}$ is

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

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

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