$\large \displaystyle\int _{ 0 }^{ 1 }{ \displaystyle\int _{ 0 }^{ 1 }{ x\left\{ \dfrac { 1 }{ 1-xy } \right\} \, dx\; dy } } =A-\dfrac { \zeta (B) }{ C }$

If the equation above holds true for positive integers $A,B$ and $C$, find $A\times B \times C$.

**Notations**:

$\{ \cdot \}$ denotes the fractional part function.

$\zeta(\cdot)$ denotes the Riemann zeta function.