Who's up to the challenge? 27

0101{xy}{yx}dxdy=Aζ(B)C \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,BA,B and CC. Find A+B+CA+B+C.

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