If $2 \cos ^2 \theta+3 \cos \theta=2$, then permissible value of $\cos \theta$ is

The principal solutions of $\cot x=\sqrt{3}$ are

$$\tan A+2 \tan 2 A+4 \tan 4 A+8 \cot 8 A=$$

The values of $x$ in $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\sin x \cos x=\frac{1}{4}$ are ..........