If $\tan \theta + \tan 2\theta + \sqrt 3 \tan \theta \tan 2\theta = \sqrt 3 ,$ then

Number of values of $x$ satisfying $2sin^22x = 2cos^28x + cos10x$ in $x  \in \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is-
 

If $\sqrt{3}\left(\cos ^{2} x\right)=(\sqrt{3}-1) \cos x+1,$ the number of solutions of the given equation when $x \in\left[0, \frac{\pi}{2}\right]$ is

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 $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is

If $\cos \theta + \cos 2\theta + \cos 3\theta = 0$, then the general value of $\theta $ is