JEE Math Practice Question

Let $ A = \left\{ \theta \in [0, 2\pi] : 1 + 10\operatorname{Re}\left( \frac{2\cos\theta + i\sin\theta}{\cos\theta - 3i\sin\theta} \right) = 0 \right\} $. Then $ \sum\limits_{\theta \in A} \theta^2 $ is equal to

1. A.$ \frac{21}{4} \pi^2 $
2. B.$ 6\pi^2 $
3. C.$ \frac{27}{4} \pi^2 $
4. D.$ 8\pi^2 $