If $12{\cot ^2}\theta - 31\,{\rm{cosec }}\theta + {\rm{32}} = {\rm{0}}$, then the value of $\sin \theta $ is

  • A

    $\frac{3}{5}$ or $1$

  • B

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

  • C

    $\frac{4}{5}$ or $\frac{3}{4}$

  • D

    $ \pm \frac{1}{2}$

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The general solution of $\tan 3x = 1$ is

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  • [JEE MAIN 2019]