Hello,
In Mathematica,
ArcTan[Tan[Pi/6]]
will produce Pi/6.
Pi/6
But
FullSimplify@ArcTan[Tan[\[Theta]]]
only produces
ArcTan[Tan[\[Theta]]]
What is the problem of the latter?
The equality
ArcTan[Tan[\[Theta]]] == \[Theta]
is true only when -Pi/2 < \[Theta] < Pi/2:
-Pi/2 < \[Theta] < Pi/2
Simplify[ArcTan[Tan[\[Theta]]], -Pi/2 < \[Theta] < Pi/2]
May you tell why this works?
Try
ArcTan[Tan[Pi/6 + Pi]]
