Solve $\cos t=24\sum_{n=1}^{\infty}\frac{ny^n(\cos(t+nz)-y\cos t))}{1-2y^n\cos(nz)+y^{2n}}$ for $t$

Question

Let $t\in\left(\frac{\pi}3,\frac{2\pi}3\right)$. Let $y:=e^{-2\pi\sin t}$. Let $z:=2\pi\cos t$. Solve $$\cos t=24\sum_{n=1}^{\infty}\frac{ny^n(\cos(t+nz)-y\cos t))}{1-2y^n\cos(nz)+y^{2n}}.$$

One solution is $t=\frac{\pi}2$.

This came up when trying to find $\max|\Delta|$ on the fundamental domain.