I think what you're wondering is why you're not getting a result like
23*%pi/45 or whatever.
First of all, in the particular case you're showing, I don't think there is
a nice, clean, simple result like that.
But secondly, Maxima currently doesn't simplify using all the acos
identities it should.
For example,
acos(1/sqrt(2)) = acos(sqrt(2)/2) = %pi/4
but Maxima does not currently perform this simplification, not to mention
more complicated cases. (Perhaps there is a share package that does this?)
-s