AMC 12 2004a Problem 21

If $\sum_{n = 0}^{\infty}\cos^{2n}\theta = 5$, what is the value of $\cos{2\theta}$?

$\text {(A) } \frac15 \text {(B) } \frac25 \text {(C) } \frac {\sqrt5}{5} \text {(D) } \frac35 \text {(E) }\frac45$