Tricky Trig

Geometry Level 4

The sum of all positive solutions of 2cos2x(cos2xcos2014π2x)=cos4x1 2\cos 2x \left( \cos 2x- \cos\frac { 2014 \pi ^ 2 }{ x } \right) =\cos { 4x } -1 is kπk\pi . Find kk.

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