If $7 \sin ^{2} \theta+3 \cos ^{2} \theta=4\left(0^{\circ} \leq \theta \leq 90^{\circ}\right)$, then value of $\theta$ is

$7 \sin ^{2} \theta+3 \cos ^{2} \theta=4$

$\Rightarrow 7 \sin ^{2} \theta+3\left(1-\sin ^{2} \theta\right)=4$

$\Rightarrow 7 \sin ^{2} \theta+3-3 \sin ^{2} \theta=4$

$\Rightarrow 4 \sin ^{2} \theta=4-3=1$

$\Rightarrow \sin ^{2} \theta=\frac{1}{4} \Rightarrow \sin \theta=\frac{1}{2}=\sin \frac{\pi}{6} \Rightarrow \theta=\frac{\pi}{6}$