Well, it IS helpful to have an understanding of "all" math if you're going into game dev...
Pythagoras may have been a weenie, but pythagorean theorem is pretty much all basic Trigonometry is. Don't forget! When it comes to finding the sin or tan, it's always opp on top! (opposite side divided by hyp. OR opposite side divided by the adjacent side. opp/hyp and opp/adj hence the "opp on top") Nobody's saying you HAVE to memorize the entire table of trigonometric ratios either, but 45 degree triangles are pretty easy. .707 .707 1 ratios. It's also helpful to know your radians and degrees. Advanced Trigonometry should teach you all sorts of tools, though I've only done basic Trig so far so I can't vouch for it.
Half of Trig is basically what you learn in honors 6th grade too, if that helps (assuming you had honors 6th grade). Though, trying to remember middle school classes is probably an even bigger hassle than learning Trigonometry.
All problems have an answer key, and some problems are solved. If you can do the homework problems, you are good to go with your trig knowledge. There are still a few tricks I need to prepare problems for, but if you can do that homework, you should be prepared enough to be able to read wikipedia and will no longer need any help.
The lecture is a bit long - I teach it for a total of 2 long or 3 short sessions - however ALL of trigonometry AND inverse trigonometry fits in that single lecture file.
I would say just hone your skills at C++ like most people have said. It's far better trying to concentrate on a dedicated skill, rather a splash of this and that :)
That part is the most useful one ... forget about the proof: did you get the slide that shows how to use the above formula (called the Euler formula) to derive other trig formulas?