In this blog we will prove a mysterious identity:

$$$\sum\limits_{n_1 \in \mathbb{Z}}(-1)^{n_1}\sum\limits_{(n_2, n_3) \in \mathbb{Z}^2}\frac{1}{\sqrt{n_1^2+ (n_2+0.5)^2+(n_3+0.5)^2}\sinh{\pi\sqrt{n_1^2+ (n_2+0.5)^2+(n_3+0.5)^2}}} = 1$$$.