The number of solutions of the equation $\sin 2x - 2 \cos x + 4 \sin x = 4$ in the interval $[0, 5\pi]$ is

Let $\theta \in [0, 4\pi ]$ satisfy the equation $(\sin \theta + 2) (\sin \theta + 3) (\sin \theta + 4) = 6$. If the sum of all the values of $\theta$ is of the form $k\pi$,then the value of $k$ is:

Let $S$ be the sum of all solutions (in radians) of the equation $\sin^{4} \theta + \cos^{4} \theta - \sin \theta \cos \theta = 0$ in $[0, 4\pi]$. Then $\frac{8S}{\pi}$ is equal to ...... .

The number of solutions of the equation $\sec x = 1 + \cos x + \cos^2 x + \dots \infty$ in the interval $x \in [-50 \pi, 50 \pi]$ is -

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 $\sin 6 \theta + \sin 4 \theta + \sin 2 \theta = 0$,then the general value of $\theta$ is