The sum of all values of $x$ in $[0,2 \pi]$, for which $\sin x+\sin 2 x+\sin 3 x+\sin 4 x=0$, is equal to:

  • [JEE MAIN 2021]
  • A

    $11 \pi$

  • B

    $12 \pi$

  • C

    $8 \pi$

  • D

    $9 \pi$

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  • [JEE MAIN 2022]