**Solution 1.** We follow the proof of Jensen's formula that is given in the book. We keep step 1 exactly the same. Following step 2, we have set $g=f / \psi_1 \cdot \psi_N$, then $g$ is holomorphic and bounded near each $z_j$. So it suffices to prove the theorem for Blaschke factors and for bounded functions that vanish nowhere. Functions that vanish nowhere are treated in Step 3. It remains to show the result for Blaschke factors. We have
\[
\log \left|\psi_\alpha(0)\right|=\log |\alpha|=\log |\alpha|+\frac{1}{2 \pi} \int_0^{2 \pi} \log \left|\psi_\alpha\left(e^{i \theta}\right)\right| d \theta,
\]
since $\left|\psi_\alpha(z)\right|=1$ for $z \in \partial \mathbb{D}$.