If the system of linear equations $(\sin \theta) x-y+z=0, x-(\cos \theta) y+z=0$, $x+y+(\sin \theta) z=0$ has non-trivial solution, then the least positive value of $\theta$ is

• A

  $\frac{\pi}{6}$
• B

  $\frac{\pi}{4}$
• C

  $\frac{\pi}{3}$
• Correct answer
  D

  $\frac{\pi}{2}$

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