Let $f(x) = sinx + 2sin^2x + 3sin^3x + 4sin^4x+....\infty $ , then number of solution $(s)$ of equation $f(x) = 2$ in $x \in \left[ { - \pi ,\pi } \right] - \left\{ { \pm \frac{\pi }{2}} \right\}$ is

If the equation $2tan\ x \ sin\ x -2 tan\ x + cos\ x = 0$ has $k$ solutions in $[0,k \pi]$, then number of integral values of $k$ is-

$\cot \theta = \sin 2\theta (\theta \ne n\pi $, $n$ is integer), if $\theta = $

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

$\sin 6\theta + \sin 4\theta + \sin 2\theta = 0,$ then $\theta = $

If $\sin 2x + \sin 4x = 2\sin 3x,$ then $x =$