Let $S={\theta \in\left(0, \frac{\pi}{2}\right): \sum_{m=1}^{9}}$

$\sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}$ Then.

  • [JEE MAIN 2022]
  • A

    $S =\left\{\frac{\pi}{12}\right\}$

  • B

    $S =\left\{\frac{2 \pi}{3}\right\}$

  • C

    $\sum_{\theta \in S} \theta=\frac{\pi}{2}$

  • D

    $\sum_{\theta \in S} \theta=\frac{3 \pi}{4}$

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