\[\large \int _{ 1 }^{ {e}^{\pi /4} }{ \cfrac { \tan ( \ln { x } ) }{ x } } \, dx = \, \dfrac{A}{B} \, \ln C\]

Given \(A\), \(B\) and \(C\) are positive integers satisfying the equation above, with \(A\) and \(B\) coprime and \(C\) minimised, find \(A+B+C\).

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