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

  • A

    $\frac{\pi }{6}$

  • B

    $\frac{\pi }{3}$

  • C

     $\frac{\pi }{3}$ or $\frac{\pi }{6}$

  • D

     $\frac{\pi }{3}$ or $\frac{2\pi }{3}$

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