Evaluate the following sum

\(\displaystyle\sum_{m=1}^\infty \sum_{\substack{n\ge 1\\ (m,n)=1}} \frac{x^{m-1}y^{n-1}}{1-x^m y^n}\)

when |x|, |y|<1.

(We write (m,n) to denote the g.c.d of m and n.)