If $\cos \theta = \frac{-1}{2}$ and $0^o < \theta < 360^o$,then the values of $\theta$ are

The principal solutions of $\text{cosec}(\theta) = -2$ are...

If $\sec 4\theta - \sec 2\theta = 2$,then the general value of $\theta$ is

The number of solutions of the equation $\sec x = 1 + \cos x + \cos^2 x + \dots \infty$ in the interval $x \in [-50 \pi, 50 \pi]$ is -

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

Let $S = \left[-\pi, \frac{\pi}{2}\right) - \left\{-\frac{\pi}{2}, -\frac{\pi}{4}, -\frac{3\pi}{4}, \frac{\pi}{4}\right\}$. Then the number of elements in the set $\{\theta \in S : \tan \theta(1 + \sqrt{5} \tan(2\theta)) = \sqrt{5} - \tan(2\theta)\}$ is: