If $\sin \theta = \sqrt 3 \cos \theta , - \pi < \theta < 0$, then $\theta = $
$ - \frac{{5\pi }}{6}$
$ - \frac{{4\pi }}{6}$
$\frac{{4\pi }}{6}$
$\frac{{5\pi }}{6}$
The number of roots of the equation $\cos ^7 \theta-\sin ^4 \theta=1$ that lie in the interval $[0,2 \pi]$ is
The number of solutions of the equation $1 + {\sin ^4}\,x = {\cos ^2}\,3x,x\,\in \,\left[ { - \frac{{5\pi }}{2},\frac{{5\pi }}{2}} \right]$ is
Values of $\theta (0 < \theta < {360^o})$ satisfying ${\rm{cosec}}\theta + 2 = 0$ are
The number of values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ such that $\theta \neq \frac{n \pi}{5}$ for $n=0, \pm 1, \pm 2$ and $\tan \theta=\cot 5 \theta$ as well as $\sin 2 \theta=\cos 4 \theta$ is
If $\cos \theta + \cos 2\theta + \cos 3\theta = 0$, then the general value of $\theta $ is