求 \(\displaystyle\sum_{n\geq 1} \prod_{k=1}^{2n-1}\cos^2(\frac{k\pi}{4n})\)

elim

题：计算 \(\displaystyle\sum_{n\geq 1} \prod_{k=1}^{2n-1}\cos^2(\frac{k\pi}{4n})\)

永远

呵呵………