The number of solutions of the equation $\sin A - 5 \sin 2A + \sin 3A = \cos A - 5 \cos 2A + \cos 3A$ in the interval $(0, \pi)$ is:

If the sum of solutions of the system of equations $2 \sin^{2} \theta - \cos 2\theta = 0$ and $2 \cos^{2} \theta + 3 \sin \theta = 0$ in the interval $[0, 2\pi]$ is $k\pi$,then $k$ is equal to.

Find the principal and general solutions of the equation $\tan x = \sqrt{3}$.

If $5\cos^2 \theta + 7\sin^2 \theta - 6 = 0$,then the general value of $\theta$ is

The number of solutions of the equation $\cos 2 \theta \cos \frac{\theta}{2} + \cos \frac{5 \theta}{2} = 2 \cos^3 \frac{5 \theta}{2}$ in the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is:

The number of values of $x$ for which $\sin 2x + \sin 4x = 2$ is