USAMO 1992 Problem 2

Let $\mathrm{k}=1^{0}$. Show that $\Sigma_{0}^{88} 1 /(\cos \mathrm{nk} \cos (\mathrm{n}+1) \mathrm{k})=\cos \mathrm{k} / \sin ^{2} \mathrm{k}$.