2014 AMC 12B 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 \qquad\textbf{(B)}\ 810\pi \qquad\textbf{(C)}\ 1008\pi \qquad\textbf{(D)}\ 1080 \pi \qquad\textbf{(E)}\ 1800\pi

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.