I know about oneitis and about "plenty of other fish in the sea" but realistically speaking there aren't any other options for me to choose from at the moment. So I've decided to go for her and will do anything I can.

Had she been single/had i not known about her boyfriend, I'd have directly approached and tried to run game as well as possible.

But now my concern is how to approach her and still address the elephant in the room that I know she's not single? Should I need to address it in the first place? Or treat it as a non issue?

(Context: i know her from the library where I go to study, we recognise each other but haven't talked yet. It's been less than a month since I started going there and had an exam coming up which is why I didn't approach this long. Now that's no longer the case and I was literally going to approach her today and this happened. Drew me into such a bad mood that i didn't even look at her when we passed. I imagine I looked a bit bitter, and i regret not controlling myself, but it was like less than five minutes after I saw them... I'm fucking 25 and still have so much to learn :/ I mean how immature is it that, for a short span of time, I actually felt a little angry/resentful towards the very girl I wish to fuck lol.)

So given this, what are some pointers to approach her anyway?

Thanks, and sorry if this post is too long.