The number of values of $\theta \in (0,\pi)$ for which the system of linear equations
$x + 3y + 7z = 0$
$-x + 4y + 7z = 0$
$(sin\,3\theta )x + (cos\,2\theta )y + 2z = 0$ has a non-trivial solution, is

  • [JEE MAIN 2019]
  • A

    $3$

  • B

    $2$

  • C

    $4$

  • D

    $1$

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  • [JEE MAIN 2021]

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