If $\frac{1}{6}\sin \theta$, $\cos \theta$ and $\tan \theta$ are in geometric progression, then the complete solution set of $\theta$ is

• A

  $\left\{\theta :\theta =2n\pi \pm \left(\frac{\pi }{6}\right), n\in I\right\}$
• Correct answer
  B

  $\left\{\theta :\theta =2n\pi \pm \left(\frac{\pi }{3}\right), \mathrm{n }\mathrm{\in }I\right\}$
• C

  $\left\{\theta :\theta =n\pi +{\left(-1\right)}^n\left(\frac{\pi }{3}\right), \mathrm{n }\mathrm{\in }I\right\}$
• D

  $\left\{\theta :\theta =n\pi +\frac{\pi }{3}, \mathrm{n }\mathrm{\in }I\right\}$

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