$$2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)$$, then $$\tan \theta=$$

The principal solutions of $$\sqrt{3} \sec x+2=0$$ are

If $$x \in\left(0, \frac{\pi}{2}\right)$$ and $$x$$ satisfies the equation $$\sin x \cos x=\frac{1}{4}$$, then the values of $$x$$ are

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