The perimeter of a $\triangle ABC$ is $6$ times the arithmetic mean of the sine of its angles. If its side $BC$ is of unit length,then $\angle A=$

  • A
    $\frac{\pi}{6}$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{\pi}{2}$
  • D
    $\pi$

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