How do you 'nicely' ask someone what their problem is?

Anonymous
There's a girl that's become friends with some guy friends of mine in the past year. She seems really cool, like we'd get along really well. I know that she's made really great friends with one guy who really dislikes me, and I believe that has a bit to do with it. I've always heard she's friendly and outgoing, but around me she has hardly said a word or acknowledged me. We now go to the same University, and any time I notice her, she's staring me down. By the time I'm able to let out a smile, she has already turned away. How can I ask her what her problem is with me? It's really hurt a few of my friendships, and I don't want us to hate each other. I just want to know what the deal is.
How do you 'nicely' ask someone what their problem is?
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