Answer
$2-\sqrt3$
Work Step by Step
Using the given formula and the known values: $\tan (-345^\circ)=\frac{\tan 45^\circ-\tan 390^\circ}{1+\tan 45^\circ\tan 390}=\frac{1-\frac{1}{\sqrt3}}{1-1\frac{1}{\sqrt3}}=2-\sqrt3$
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