prove tan 20 tan 40 tan 80 = tan 60 Without using a calculator

We have a simple formula in our books as follows:- Tanθ.tan(60-θ).tan(60+θ) = tan3θ We see a similar situation in the question, let 20°=θ ,then 40°=60-θ and 80°=60+θ.So it turna out to tan3θ which is tan3(20) =tan60. Please approve it it helpedThanks