I saw this trigonometry question a few days ago.

$\mathrm{tan}1^{\circ} \mathrm{tan}2^{\circ} \mathrm{tan}3^{\circ} \ldots \mathrm{tan}88^{\circ} \mathrm{tan}89^{\circ} = ?$

Hint: $\mathrm{tan}(90^{\circ} - \theta) = \mathrm{cot} \theta$