Riemann- zeta function (III)

True or false? $\displaystyle \frac{-1}{2} \left (\pi z \cot (\pi z) - 1 \right) = \sum_{n = 1}^{\infty} \zeta (2n) z^{2n}$ in $D(0, 1) \subset \mathbb{C}$ , after eliminating the avoidable singularity of $\pi z \cot (\pi z)$ at $z = 0$ .

Note.-

a) $\zeta ( \cdot )$ is Riemann zeta function .

b) we are assuming Axiom of Choice according to main principles of "constructive mathematics".