Find the sum of all the positive solutions of    
\[2\cos2x \left(\cos2x - \cos{\left( \frac{2014\pi^2}{x} \right) } \right) = \cos4x - 1\]    
If the answer is \(x\pi\), what is the value of \(x\)?

Let's think step by step and output the final answer within \boxed{}.
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