Prove the following identity for \( x, y \in \mathbb{R}^3 \):
\[
\frac{1}{|x-y|} = \frac{1}{\pi^3} \int_{\mathbb{R}^3} \frac{1}{|x-z|^2} \frac{1}{|y-z|^2} dz.
\]

Solutions are due May 6th (Friday), 6PM, and it will remain open if nobody solved it.