$\begin{aligned} & f(\theta)=\frac{\sin ^4 \theta+3 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta} \\ & f(\theta)=1+\frac{2 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta} \\ & f(\theta)=\frac{2 \cos ^2 \theta}{\cos ^4 \theta-\cos ^2 \theta+1}+1 \\ & f(\theta)=\frac{2}{\cos ^2 \theta+\sec ^2 \theta-1}+1 \\ & \left.f(\theta)\right|_{\text {min. }}=1 \\ & f(\theta)_{\text {max. }}=3 \\ & S=\frac{64}{1-1 / 3}=96\end{aligned}$