If $\tan \theta = – \frac{1}{{\sqrt 3 }}$ and $\sin \theta = \frac{1}{2}$, $\cos \theta = – \frac{{\sqrt 3 }}{2}$, then the principal value of $\theta $ will be

$sin 3\theta = 4 sin\, \theta \,sin \,2\theta \,sin \,4\theta$ in $0\, \le \,\theta\, \le \, \pi$ has :

The number of solutions to $\sin \left(\pi \sin ^2 \theta\right)+\sin \left(\pi \cos ^2 \theta\right)=2 \cos \left(\frac{\pi}{2} \cos \theta\right)$ satisfying $0 \leq \theta \leq 2 \pi$ is

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

If $2(\sin x – \cos 2x) – \sin 2x(1 + 2\sin x)2\cos x = 0$ then