Tan 15° = Tan(45 – 30)°

Tan (A – B) = (Tan A – Tan B) /(1 + Tan A Tan B)

Therefore,,

tan(45 – 30)° = tan 45° – tan 30°/1+tan 45° tan 30°

Now putting the values of tan 45° and tan 30° from the table we get;

tan(45 – 30)° = (1 – 1/√3)/ (1 + 1.1/√3)

tan (15°) = √3 – 1/ √3 + 1