Simplifying a trigonometric function with arctan

Question

Why is this trigonometric expression with $\arctan$ not simplified ?

ArcTan[Tan[γ[t] - θ[t]]]

Answer 1

Note

Plot[{ArcTan[Tan[a]], a}, {a, -Pi, Pi},
 PlotLegends -> "Expressions"]

Consequently, some assumptions are needed to get the simplification

Assuming[{-Pi/2 < γ[t] - θ[t] < Pi/2}, 
 Simplify[ArcTan[Tan[γ[t] - θ[t]]]]]

(*  γ[t] - θ[t]  *)

Or use PowerExpand

ArcTan[Tan[γ[t] - θ[t]]] // PowerExpand

(*  γ[t] - θ[t]  *)