QJEEM25Mae358: JEE Main 2025 Mathematics - Class 11 JEEM25Mae358 Solution: The sum of all values of satisfying and is

$\begin{aligned}& 2 \sin ^2 \theta=\cos 2 \theta \\& 2 \sin ^2 \theta=1-2 \sin ^2 \theta \\& 4 \sin ^2 \theta=1 \\& \sin ^2 \theta=\frac{1}{4} \\& \sin \theta= \pm \frac{1}{2} \\& 2 \cos ^2 \theta=3 \sin \theta \\& 2-2 \sin ^2 \theta+3 \sin \theta-2=0 \\& (2 \sin \theta-1)(2 \sin \theta-2)=0 \\& \sin \theta=\frac{1}{2}\end{aligned}$

so common equation which satisfy both equations is $\sin \theta=\frac{1}{2}$

$\theta=\frac{\pi}{6}, \frac{5 \pi}{6} \quad(\theta \in[0,2 \pi])$

$\text { Sum }=\pi$