$2 \sin ^{2} \theta-\cos 2 \theta=0$

$2 \sin ^{2} \theta-\left(1-2 \sin ^{2} \theta\right)=0$

$\sin ^{2} \theta=\left(\frac{1}{2}\right)^{2}$

$\theta=\frac{\pi}{6}, \frac{5 \pi}{6}, \frac{7 \pi}{6}, \frac{11 \pi}{6}$

$2 \cos ^{2} \theta+3 \sin \theta=0$

$2 \sin ^{2} \theta-3 \sin \theta-2=0$

$\therefore \sin \theta=-\frac{1}{2}$

$\theta=\frac{7 \pi}{6}, \frac{11 \pi}{6}$

So, the common solution is

$\theta=\frac{7 \pi}{6}, \frac{11 \pi}{6}$

$\text { Sum }=\frac{7 \pi+11 \pi}{6}=3 \pi= k \pi$

$K =3$