The solution set of the equation $tan(\pi\, tanx) = cot(\pi\, cot\, x)$ is

  • A

    $\phi $

  • B

    $\{0\}$

  • C

    $\left\{ {\frac{\pi }{4}} \right\}$

  • D

    none of these

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  • [JEE MAIN 2013]

If $1\,\, + \,\,\sin \theta \,\, + \,\,{\sin ^2}\theta  +  \ldots .\,\,to\,\,\infty \,\, = \,\,4\, + 2\sqrt 3 ,\,\,0\,\, < \,\theta \,\,\pi ,\,\,\theta \,\, \ne \,\frac{\pi }{2}\,,$ then $\theta  = $