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

If $|k|\, = 5$ and ${0^o} \le \theta \le {360^o}$, then the number of different solutions of $3\cos \theta + 4\sin \theta = k$ is

Let $\theta \in [0, 4\pi ]$ satisfy the equation $(sin\, \theta + 2) (sin\, \theta + 3) (sin\, \theta + 4) = 6$ . If the sum of all the values of $\theta $ is of the form $k\pi $, then the value of $k$ is

The general solution of the equation $sin^{100}x\,-\,cos^{100} x= 1$ is

If $4{\sin ^2}\theta + 2(\sqrt 3 + 1)\cos \theta = 4 + \sqrt 3 $, then the general value of $\theta $ is

The number of real solutions $x$ of the equation $\cos ^2(x \sin (2 x))+\frac{1}{1+x^2}=\cos ^2 x+\sec ^2 x$ is