Thanks for being so nice about me not explaining in the manner you require, my bad. But as to the 'huh', I was firstly confused at how your statement followed from the equation, and secondly confused at why I would/should observe that fact to solve the equation. Is that the only way? Or do you suggest that to be the easiest way? I don't know. But I do know this follows from that observation -
and
and
and
and since the arccos of both 1 and -1 is
(or more specifically
and
where
is even and
is odd) I would now have to find
- so unless there is an algebraic method for doing that, splitting the equation in two doesn't help me. Is there anything else you can recommend?