(C) 60°
$7\cos^2\theta + 3\sin^2\theta = 4 \Rightarrow 7\cos^2\theta + 3(1-\cos^2\theta) = 4 \Rightarrow 4\cos^2\theta = 1 \Rightarrow \cos\theta = \dfrac{1}{2} \Rightarrow \theta = 60°$
Replace $\sin^2\theta$ with $1-\cos^2\theta$, simplify to get $\cos\theta = \frac{1}{2}$, which gives $\theta = 60°$. This is a standard identity-based MCQ; remember the standard angle values table from Chapter 8.