If ${\sin ^2}\theta - 2\cos \theta + \frac{1}{4} = 0,$ then the general value of $\theta $ is
$n\pi \pm \frac{\pi }{3}$
$2n\pi \pm \frac{\pi }{3}$
$2n\pi \pm \frac{\pi }{6}$
$n\pi \pm \frac{\pi }{6}$
If $\tan m\theta = \tan n\theta $, then the general value of $\theta $ will be in
$2{\sin ^2}x + {\sin ^2}2x = 2,\, - \pi < x < \pi ,$ then $x = $
Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$ If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal
If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is
If $\sin 2x + \sin 4x = 2\sin 3x,$ then $x =$