If $2\sin \theta + \tan \theta = 0$, then the general values of $\theta $ are
$2n\pi \pm \frac{\pi }{3}$
$n\pi ,2n\pi \pm \frac{{2\pi }}{3}$
$n\pi ,2n\pi \pm \frac{\pi }{3}$
$n\pi ,\,\,n\pi + \frac{{2\pi }}{3}$
The number of all possible values of $\theta$, where $0<\theta<\pi$, for which the system of equations
$ (y+z) \cos 3 \theta=(x y z) \sin 3 \theta $
$ x \sin 3 \theta=\frac{2 \cos 3 \theta}{y}+\frac{2 \sin 3 \theta}{z} $
$ (x y z) \sin 3 \theta=(y+2 z) \cos 3 \theta+y \sin 3 \theta$ have a solution $\left(\mathrm{x}_0, \mathrm{y}_0, \mathrm{z}_0\right)$ with $\mathrm{y}_0 \mathrm{z}_0 \neq 0$, is
If $2{\sin ^2}\theta = 3\cos \theta ,$ where $0 \le \theta \le 2\pi $, then $\theta = $
One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval
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
The number of solutions of $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is.