Can you use a calculator? There are many approximation methods, the most common I think to use for this would be the Taylor series for tangent.
I really don't know how your teacher wants you to do this. You could use the difference formula for tan(120-20) since 120deg = (2pi)/3 and 20deg=pi/9. Have you guys been doing angle sums in class?
edit: If you can't give some sort of direction then it won't be able to fully help you as like I said there are many ways to approximate trig functions. I can help you but I need info.