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

If $\sin 5x + \sin 3x + \sin x = 0$,then the value of $x$ other than $0$ lying between $0 \le x \le \frac{\pi}{2}$ is

If angle $\theta$ in $[0, 2\pi]$ satisfies both the equations $\cot \theta = \sqrt{3}$ and $\sqrt{3} \sec \theta + 2 = 0$,then $\theta$ is equal to

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 solutions of the equation $4 \cos 2 \theta \cdot \cos 3 \theta = \sec \theta$,when $0 < \theta < \pi$,is

The number of solutions of the equation $(4-\sqrt{3}) \sin x - 2 \sqrt{3} \cos^2 x = -\frac{4}{1+\sqrt{3}}$ for $x \in [-2\pi, \frac{5\pi}{2}]$ is