How does the angle γ change under inversion in Euler angles?

[ftft]

The well known Euler angles (αβγ) are defined as in the image

It is easy to see that under inversion
α → π+α
β → π-β
but I cannot figure out how γ transforms under inversion. actually I am stuck at the question whether I should measure it from the same intersection line ON (thence γ →π+γ) or if the latter is also inverted (I think then I will have γ→γ)

 

[The Bill]

First, I'm not convinced that the two formulas you have are, in fact, "easy to see." Second, I don't understand how this question falls under the category of topology or analysis.

 

[ftft]

Oops! Then I am moving my question to general math