Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$.

Then $\sum_{\theta \in S } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to

  • [JEE MAIN 2023]
  • A

    $4$

  • B

    $6$

  • C

    $8$

  • D

    $2$

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