If $2 \sin 2 \theta = \sqrt{3}$,then $\theta = $ (in $^{\circ}$)

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

If the solution of the equation $\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1$,where $x \in \left(0, \frac{\pi}{2}\right)$,is $\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$,where $\alpha, \beta$ are integers,then $\alpha+\beta$ is equal to:

The solutions of $\sin x + \sin 5x = \sin 3x$ in the interval $(0, \frac{\pi}{2})$ are

The solution of $3 \tan (A - 15^{\circ}) = \tan (A + 15^{\circ})$ is

Find the general solution of $\csc x = -2$.