If $\sin 2\theta = \cos 3\theta $ and $\theta $ is an acute angle, then $\sin \theta $ is equal to

Find the solution of $\sin x=-\frac{\sqrt{3}}{2}$

The number of solutions that the equation $sin5\theta cos3\theta  = sin9\theta cos7\theta $ has in $\left[ {0,\frac{\pi }{4}} \right]$ is

The number of values of $\theta $ in $[0, 2\pi]$ satisfying the equation $2{\sin ^2}\theta = 4 + 3$$\cos \theta $ are

For each positive real number $\lambda$. Let $A_\lambda$ be the set of all natural numbers $n$ such that $|\sin (\sqrt{n+1})-\sin (\sqrt{n})|<\lambda$. Let $A_\lambda^c$ be the complement of $A_\lambda$ in the set of all natural numbers. Then,

If $4{\sin ^2}\theta + 2(\sqrt 3 + 1)\cos \theta = 4 + \sqrt 3 $, then the general value of $\theta $ is