Who's up to the challenge? 27

Calculus Level 5

\[ \large \displaystyle\int _{ 0 }^{ 1 }{ \int _{ 0 }^{ 1 }{ \left \{ \frac { x }{ y } \right\} \left \{ \frac { y }{ x } \right \} \, dxdy=A-\dfrac { \zeta (B) }{ C } } } \]

The equation above holds true for positive integers \(A,B\) and \(C\). Find \(A+B+C\).

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