Number of solutions of $\sqrt {\tan \theta } = 2\sin \theta ,\theta \in \left[ {0,2\pi } \right]$ is equal to
$2$
$4$
$5$
$6$
If $\alpha ,\,\beta ,\,\gamma $ and $\delta $ are the solutions of the equation $\tan \left( {\theta + \frac{\pi }{4}} \right) = 3\,\tan \,3\theta $ , no two of which have equal tangents, then the value of $tan\, \alpha + tan\, \beta + tan\, \gamma + tan\, \delta $ is
If $(1 + \tan \theta )(1 + \tan \phi ) = 2$, then $\theta + \phi =$ ....$^o$
General solution of $\tan 5\theta = \cot 2\theta $ is $($ where $n \in Z )$
If equation in variable $\theta, 3 tan(\theta -\alpha) = tan(\theta + \alpha)$, (where $\alpha$ is constant) has no real solution, then $\alpha$ can be (wherever $tan(\theta - \alpha)$ & $tan(\theta + \alpha)$ both are defined)
If $\sin \theta + 2\sin \phi + 3\sin \psi = 0$ and $\cos \theta + 2\cos \phi + 3\cos \psi = 0$ , then the value of $\cos 3\theta + 8\cos 3\phi + 27\cos 3\psi = $