(2) (a) Let $f(z)$ be an entire function and $R > 0$. For $\alpha, \beta \in \mathbb{C}$ inside $C_R(0)$, prove the following identity.
$\frac{1}{2\pi i} \int_{C_R(0)} \frac{f(z)}{(z - \alpha)(z - \beta)} dz = \frac{f(\alpha) - f(\beta)}{\alpha - \beta}$
(b) Furthermore, when $f(z)$ is bounded, use the above equation to provide an alternative proof of Liouville's theorem.