If $\tan \theta + \tan 2\theta + \sqrt 3 \tan \theta \tan 2\theta = \sqrt 3 ,$ then
$\theta = (6n + 1)\pi /18,\,\forall n \in I$
$\theta = (6n + 1)\pi /9,\,\forall n \in I$
$\theta = (3n + 1)\pi /9,\,\forall n \in I$
None of these
The number of elements in the set $S=$ $\left\{\theta \in[-4 \pi, 4 \pi]: 3 \cos ^{2} 2 \theta+6 \cos 2 \theta-\right.$ $\left.10 \cos ^{2} \theta+5=0\right\}$ is
Let $S=\{x \in R: \cos (x)+\cos (\sqrt{2} x)<2\}$, then
The real roots of the equation $cos^7x\, +\, sin^4x\, =\, 1$ in the interval $(-\pi, \pi)$ are
If $\tan \theta + \tan 2\theta + \tan 3\theta = \tan \theta \tan 2\theta \tan 3\theta $, then the general value of $\theta $ is
If $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha ),$ then $x = $