Question

Hello, is there any way to calculate arctan (2) without using calcultor?
And what is that way?

Answer 1

short answer: no

you can always use graphical or numeric methods to find the zeros of the function

f(x) = tan(x) - 2

Then there are Taylor Series, etc.

Your best bet is just to use a calculator (online or mechanical), just as you would to fine log(12) or e^3.1 or any other such animal.

Answer 2

But anyway, if arctan(2) is the solution to a problem, just leave it as-is. That way you have the exact answer, instead of just an approximation.

And, it's clear what the value is. Saying that θ = 1.107 does not give much insight into where it came from.