Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$  If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal

  • [JEE MAIN 2022]
  • A

    $7+\sqrt{3}$

  • B

    $9$

  • C

    $8+\sqrt{3}$

  • D

    $10$

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  • [JEE MAIN 2021]

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