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Kill 'em with kindness, I always say.
If you're nice to her (say hi when you pass, invite her places, etc.), but she's really determined to hate you, she'll get even more pissed off at you simply because you're "oblivious" to the fact that she doesn't like you. But she won't say anything because she's not going to flip out on you for being friendly. And if she talks to other sisters about you, what could she possibly say that's bad?
If you walk by her, give her a friendly hello. If she comes over to your group of friends and ignores you, make it a point to ask her a question or try to talk to her. If you show her it doesn't bother you, then there's a good chance it'll start to bother her more (if she's dead-set on making you miserable and shutting you out).
And if that's the case, you can't feel bad for her. That's just how she is, and there's nothing you can do about it.
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I believe in the values of friendship and fidelity to purpose
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