We can simplify this expression using the trigonometric identity:
\[\tan(A-B) = \frac{\tan A - \tan B}{1+\tan A \tan B}\]
In this case, we have A = 80° and B = 20°. Therefore:
\[\tan(A-B) = \tan(80°-20°) = \tan 60° = \sqrt{3}\]
Using the identity, we can rewrite the expression as:
\[\frac{\tan 80° - \tan 20°}{1 + \tan 80° \tan 20°} = \tan(80°-20°) = \sqrt{3}\]
Therefore, the simplified expression is \(\sqrt{3}\).
So the correct option is (3) \(\sqrt{3}\).