The value of $\theta \in\left(0, \frac{\pi}{2}\right)$ for which the volume of the tetrahedron formed by $P(0,0,0)$, $Q(1,0, \cos \theta), R(\sin \theta,-1, a)$ and $S(\cos \theta, 0,-\sin \theta)$ is largest is

• Correct answer
  A

  $\frac{\pi}{6}$
• B

  $\frac{\pi}{4}$
• C

  $\frac{\pi}{3}$
• D

  $\frac{5 \pi}{12}$

Hence, the correct answer is option: 'A'.