The number of values of $\theta$ in $[0, 2\pi]$ satisfying the equation $2\sin^2 \theta = 4 + 3\cos \theta$ is

The number of values of $x$ in the interval $(0, 5 \pi)$ satisfying the equation $3 \sin^2 x - 7 \sin x + 2 = 0$.

If the general solution of $\sin 5x = \cos 2x$ is of the form $x = a_n \cdot \frac{\pi}{2}$ for $n = 0, \pm 1, \pm 2, \dots$,then $a_n =$

The sum of solutions in $x \in (0, 2\pi)$ of the equation $4\cos(x)\cos\left(\frac{\pi}{3} - x\right)\cos\left(\frac{\pi}{3} + x\right) = 1$ is equal to: (in $\pi$)

The number of possible solutions of $\sin \theta + \sin 4 \theta + \sin 7 \theta = 0$ for $\theta \in (0, \pi)$ is:

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