Matterwave already gave you an answer in post #18. That's why I didn't elaborate.Given that there is an operator L^2, with eigenvalue l(l+1), can you define an operator L with eigenvalue square root of l(l+1) when applied to an eigenfunction, thus telling you the total angular momentum of the system? [...]
[...] this is frustrating me that I don't have a yes or no answer.
If you still don't understand why post #18 answers your question, then feel free to ask further questions, quoting the context of that post.
Btw, in case you think I'm being too tough on you, let me say that I actually understand your situation, having been through it myself. In one u'grad course, they presumed knowledge of group theory even though the course sequence I'd been allowed to choose did not include group theory up to that point. I was close to a nervous breakdown by the end, but got through eventually.
Take a few deep breaths, and then continue...