complex analysis - Finding contour integral $ int_gamma frac{mathrm{Im} (z)}{z - alpha} dz $

I'm trying to find the contour integral
$$

\int_\gamma \frac{\mathrm{Im} (z)}{z - \alpha} dz
$$
where $ \alpha $ is a complex number such that $ 0 < |\alpha| < 2 $ and $ \gamma $ is the circle oriented in the positive sense, centred at the circle with radius 3.

I can find that
$$
\int_\gamma \frac{\mathrm{Im} (z)}{z - \alpha} dz
=
\int_0^{2\pi} \frac{e^{it}-e^{-it}}{2i} \frac{1}{e^{it}-\alpha} i e^{it} dz
$$

but the denominator is making it difficult to find the value of the contour integral. How can I proceed in this?