AMC 12 2014b Problem 25

Find the sum of all the positive solutions of $$2\cos(2x) \left(\cos(2x) - \cos\left( \frac{2014\pi^2}{x} \right)\right) = \cos(4x) - 1$$

\textbf{(A)}\ \pi \textbf{(B)}\ 810\pi \textbf{(C)}\ 1008\pi \textbf{(D)}\ 1080 \pi \textbf{(E)}\ 1800\pi