tan(4*pi/3) and arctan(4*pi/3)

tan(4*pi/3)

http://www.wolframalpha.com/input/?i=+tan%284pi%2F3%29

arctan(4*pi/3)

http://www.wolframalpha.com/input/?i=arctan%284*pi%2F3%29

tan(4*pi/3) is clearly an irrational number. How to that arctan(4*pi/3), in radians, is irrational?

http://mathworld.wolfram.com/InverseTangent.html