If $\sin \theta = \sqrt 3 \cos \theta , - \pi < \theta < 0$, then $\theta = $

If $|cos\ x + sin\ x| + |cos\ x\ -\ sin\ x| = 2\ sin\ x$ ; $x \in  [0,2 \pi ]$ , then maximum integral value of $x$ is

General solution of the equation $\cot \theta - \tan \theta = 2$ is

Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$.

Then $\sum_{\theta \in S } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to

If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is

The number of values of $x$ for which $sin2x + sin4x = 2$ is