Let $$S = \left\{\theta \in (-2\pi, 2\pi) : \cos\theta + 1 = \sqrt{3}\sin\theta\right\}$$.
Then $$\sum_{\theta \in S} \theta$$ is equal to:

A

$$\frac{2\pi}{3}$$

B

$$\frac{4\pi}{3}$$

C

$$-\frac{2\pi}{3}$$

D

$$-\frac{4\pi}{3}$$