If 7sin2θ + 3cos2θ = 4, (0° ≤ θ ≤ 90°), then the value of θ is?

Answer: Option C

$$\begin{array}{rl}& \text{7}{\sin }^2\theta +3\text{co}{\text{s}}^2\theta =4\\ & \Rightarrow \text{7}{\sin }^2\theta +3\left(\text{1}-\text{si}{\text{n}}^2\theta \right)=4\\ & \Rightarrow \text{7}{\sin }^2\theta +3-3{\sin }^2\theta =4\\ & \Rightarrow 4{\sin }^2\theta =1\\ & \Rightarrow {\sin }^2\theta =\frac{1}{4}\\ & \Rightarrow \sin \theta =\frac{1}{2}=\text{sin 3}{0}^{\circ }\\ & \theta =30^{\circ }=\frac{\pi }{6}\left[\because {\pi }^c={180}^{\circ }\right]\end{array}$$