If $\tan m\theta = \tan n\theta $, then the general value of $\theta $ will be in

The number of solutions of the equation $x +2 \tan x =\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :

The expression $(1 + \tan x + {\tan ^2}x)$ $(1 - \cot x + {\cot ^2}x)$ has the positive values for $x$, given by

Let $X=\{x \in R: \cos (\sin x)=\sin (\cos x)\} .$ The number of elements in $X$ is

The variable $x$ satisfying the equation $\left| {\sin \,x\,\cos \,x} \right| + \sqrt {2 + {{\tan }^2}\,x + {{\cot }^2}\,x}  = \sqrt 3$ belongs to the interval

Find the general solution of the equation $\sin x+\sin 3 x+\sin 5 x=0$