We set $C = \exp\left(\frac{I}{2\pi}\right)$ with $I = \int_0^{2\pi} \ln\left(\max\left\{\left|e^{i\theta}-1\right|, \left|e^{i\theta}+1\right|\right\}\right)d\theta$. For each natural integer $k \geq 2$, we set: $$\begin{aligned}
& Q_k(X) = \prod_{\zeta \in U}(X - \zeta), \\
& R_k(X) = \prod_{\zeta \in V}(X - \zeta),
\end{aligned}$$ where $U$ denotes the set of $k$-th roots of unity $\zeta$ such that $|\zeta - 1| \leq |\zeta + 1|$ and $V$ the set of $k$-th roots of unity that are not in $U$. By bounding below the quotient: $$\frac{\left\|Q_k\right\|_{\mathbb{D}} \left\|R_k\right\|_{\mathbb{D}}}{\left\|Q_k R_k\right\|_{\mathbb{D}}},$$ show that: $$C = \inf\left\{\lambda \in \mathbb{R} \left\lvert\, \begin{array}{c} \forall Q \in \mathbb{C}[X]\backslash\{0\},\quad \forall R \in \mathbb{C}[X]\backslash\{0\}, \\ \|Q\|_{\mathbb{D}} \|R\|_{\mathbb{D}} \leq \lambda^{\operatorname{deg}(QR)} \|QR\|_{\mathbb{D}} \end{array} \right.\right\},$$ where $\operatorname{deg}(QR)$ denotes the degree of $QR$.