General solution of $eq^n\, 2tan\theta \, -\, cot\theta  =\, -1$ is

The general solution of $a\cos x + b\sin x = c,$ where $a,\,\,b,\,\,c$ are constants

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

If $\sec x\cos 5x + 1 = 0$, where $0 < x < 2\pi $, then $x =$

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

Let $S=\left\{\theta \in(0,2 \pi): 7 \cos ^{2} \theta-3 \sin ^{2} \theta-2\right.$ $\left.\cos ^{2} 2 \theta=2\right\}$. Then, the sum of roots of all the equations $x ^{2}-2\left(\tan ^{2} \theta+\cot ^{2} \theta\right) x +6 \sin ^{2} \theta=0$ $\theta \in S$, is$...$