I can't think of a good title for this

Calculus Level 5

\[ \large \displaystyle \int_{0}^{1} \int_{0}^{1} \dfrac{\ln^{2} (xy)}{1-xy} \, dx \, dy \]

If the above integral can be expressed in the form \( \dfrac{a \pi^{b}}{c} \), where \( a\) and \( c \) are positive coprime integers, find \( a + b + c \).