Zeta gcd

\[\large \sum_{\gcd(n,2016)=1} \frac{1}{n^{4}} = \dfrac{a}{b}\pi^{c}\]

The equation above holds true for positive integers \(a,b\) and \(c\) with \(a,b\) coprime. Find \(a+b+c\).

Notation: \(\gcd \) denotes the greatest common divisor function.


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