The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is

$2{\sin ^2}x + {\sin ^2}2x = 2,\, - \pi < x < \pi ,$ then $x = $

The general value of $\theta $ in the equation $2\sqrt 3 \cos \theta = \tan \theta $, is

If $\sec 4\theta - \sec 2\theta = 2$, then the general value of $\theta $ is

Let,$S=\left\{\theta \in[0,2 \pi]: 8^{2 \sin ^{2} \theta}+8^{2 \cos ^{2} \theta}=16\right\}$. Then $n ( S )+\sum_{\theta \in S}\left(\sec \left(\frac{\pi}{4}+2 \theta\right) \operatorname{cosec}\left(\frac{\pi}{4}+2 \theta\right)\right)$ is equal to.

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

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