Number of solutions of $\sqrt {\tan \theta }  = 2\sin \theta ,\theta  \in \left[ {0,2\pi } \right]$ is equal to 

The general value of $\theta $ in the equation $2\sqrt 3 \cos \theta = \tan \theta $, is

If $\cos \theta + \sec \theta = \frac{5}{2}$, then the general value of $\theta $ is

Let $S=\left\{\theta \in(0,2 \pi): 7 \cos ^{2} \theta-3 \sin ^{2} \theta-2\right.$ $\left.\cos ^{2} 2 \theta=2\right\}$. Then, the sum of roots of all the equations $x ^{2}-2\left(\tan ^{2} \theta+\cot ^{2} \theta\right) x +6 \sin ^{2} \theta=0$ $\theta \in S$, is$...$

The number of solutions of equation $3cos^2x - 8sinx = 0$ in $[0, 3\pi]$ is

If $e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}$ satisfies the equation $t ^{2}-9 t +8=0,$ then the value of $\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)$ is