Maximum value of $\prod_{r=1}^n\cos a_r$ if $0\le a_1,\ldots,a_n\le\frac{\pi}{2}$ and $\prod_{r=1}^n\cot a_r = 1$
Maximum of $\cos \alpha_{1}\cdot \cos \alpha_{2}\cdot \cos \alpha_{3}....\cos \alpha_{n}.$