\(\tan (x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y}\)

\(\implies \frac{\tan 80 - \tan 20}{1 + \tan 80 \tan 20} = \tan (80 - 20) = \tan 60°\)

\(\tan 60 = \frac{\sin 60}{\cos 60} = \frac{\sqrt{3}}{2} ÷ \frac{1}{2}\)

= \(\sqrt{3}\)