Question

How do you evaluate `arctan(sqrt3/3)` without a calculator?

Answer 1

The answer is `pi/6`

Explanation:

We can do that easily by rationalizing the numerator
we get `tan^-1[(sqrt3)/3]=tan^-1[(sqrt3.sqrt3)/(3.sqrt3)]=tan^-1[3/(3.sqrt3)]=arctan(1/(sqrt3))=pi/6`