If $\sec^2 \theta = \frac{4}{3}$,then the general value of $\theta$ is

The number of common solutions of the pair of equations $2 \sin^2 \theta - 2 \cos^2 \theta + 1 = 0$ and $2 \sin^2 \theta + 3 \sin \theta - 2 = 0$ in the interval $[0, 2\pi]$ is:

The number of solutions in $[0, \frac{\pi}{2})$ of the equation $\cos 3x \cdot \tan 5x = \sin 7x$ is

If $2\sin \theta + \tan \theta = 0$,then the general values of $\theta$ are

The number of solutions of the equation $\tan x + \sec x = 2\cos x$ lying in the interval $(0, 2\pi)$ is

The number of solutions of the equation $\sin^{65}x - \cos^{65}x = -1$ for $x \in (-\pi, \pi)$ is: