TrigIdentity Intermediate

Problem - 3924
Show that $$\frac{1}{\sin 1^\circ\sin 2^\circ}+\frac{1}{\sin 2^\circ\sin 3^\circ}+\cdots+\frac{1}{\sin 89^\circ\sin 90^\circ}=\cos 1^\circ\csc^2 1^\circ$$

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