This question is from "An introduction to Hilbert spaces" for Young.
Let $\alpha$ and $\beta$ be distinct points in the unit disc $\mathbb{D}=\{z : |z| <1\}$ then using the Residue Theorem to calculate
$\int_{\partial \mathbb{D}} \frac{dz}{(z-\alpha)(z-\beta)(\overline{z}-\overline{\alpha})(\overline{z}-\overline{\beta})}$.
I know here that the integrand has three poles (I guess simple poles) at $\alpha$, $\beta$ and $0$, but not sure how to compute the residue of the integrand at each pole as we have the conjugate of $z$ which is not holomorphic.
Thank you for any hint.