Assertion $\left(\mathrm{A}\right):$ If $\sqrt{4{\sin }^4\theta +{\sin }^{2}2\theta }+4{\cos }^2\left(\frac{\pi }{4}-\frac{\theta }{2}\right)=2,$ then $\theta$ lies in $3^{\mathrm{rd}}$ quadrant or $4^{\mathrm{th}}$ quadrant.
Reason $\left(\mathrm{R}\right): \sqrt{{\sin }^2\theta }=\sin \theta$

• A

  Both $\left(\mathrm{A}\right)$ and $\left(\mathrm{R}\right)$ are true and $\left(\mathrm{R}\right)$ is the correct explanation of $\left(\mathrm{A}\right)$
• B

  Both $\left(\mathrm{A}\right)$ and $\left(\mathrm{R}\right)$ are true but $\left(\mathrm{R}\right)$ is not the correct explanation of $\left(\mathrm{A}\right)$
• Correct answer
  C

  $\left(\mathrm{A}\right)$ is true but $\left(\mathrm{R}\right)$ is false
• D

  $\left(\mathrm{A}\right)$ is false but $\left(\mathrm{R}\right)$ is true

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