Coprime distribution

Given 2 randomly generated positive integers \(a\) and \(b\), the probability that they are coprime i.e. \(\text{gcd}(a,b)=1\) can be written as \(P\). If \(P\) can be written as \(\dfrac {a}{b \pi^c}\), find \(a + b + c\) where the fraction has been reduced to lowest terms.

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