The number of solutions for the equation $\sin 2x + \cos 4x = 2$ is

If the general solution of the equation $\frac{\tan 3x - 1}{\tan 3x + 1} = \sqrt{3}$ is $x = \frac{n\pi}{p} + \frac{7\pi}{q}$ where $n, p, q \in \mathbb{Z}$,then $\frac{p}{q}$ is

If $\sin 6 \theta + \sin 4 \theta + \sin 2 \theta = 0$, then the general value of $\theta$ is

If $\cos \theta + \cos 2\theta + \cos 3\theta = 0$,then the general value of $\theta$ is

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

The general solution of $\cos 4\theta = \cos 3\theta$ is $\theta =.....$