The number of solutions of the equation $4 \sin^2 x - 4 \cos^3 x + 9 - 4 \cos x = 0$ for $x \in [-2\pi, 2\pi]$ 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.

The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $14 \operatorname{cosec}^{2} x - 2 \sin^{2} x = 21 - 4 \cos^{2} x$ holds,is

If $0 < \theta < \frac{\pi}{2}$,then the solution of the equation $\sin \theta - 3 \sin 2 \theta + \sin 3 \theta = \cos \theta - 3 \cos 2 \theta + \cos 3 \theta$ is

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

The general solution of $\frac{1-\cos 2x}{1+\cos 2x}=3$ is