If $0 \le x < \frac{\pi}{2}$,then the number of values of $x$ for which $\sin x - \sin 2x + \sin 3x = 0$ is

Find the principal solutions of the equation $\sin x = \frac{\sqrt{3}}{2}$.

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

If the general solution of $\sin 5x = \cos 2x$ is of the form $x = a_n \cdot \frac{\pi}{2}$ for $n = 0, \pm 1, \pm 2, \dots$,then $a_n =$

The number of solutions of $\sin^{7} x + \cos^{7} x = 1$ for $x \in [0, 4\pi]$ is equal to:

The sum of all $x \in [0, \pi]$ which satisfy the equation $\sin x + \frac{1}{2} \cos x = \sin^2(x + \frac{\pi}{4})$ is