Fractional Party! 1

Calculus Level 5

\[\large \int_0^1 \int _{ 0 }^{ 1 }{ { \left\{ \dfrac { x }{ y } \right\} }^{ 3 }{ \left\{ \dfrac { y }{ x } \right\} }^{ 3 } \, dx \; dy } =A-\dfrac { { \pi }^{ B } }{ C } -\dfrac { { \pi }^{ B+2 } }{ D } -\zeta \left( E \right) \]

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

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