How can I become her friend again?

In my school there is this girl named Brianna. Going way back to third grade, we we're the best of friends, working together, some hugs, talking, sticking up for eachother and never hurt eachother. I ended up falling for her and I was obsessed with her. Then she met this girl, she abandoned me and she got my finger cut and it got infected and we have hated eachother for a long time now. Everyone knows we hate eachother. But I really want to be her friend again....how can I become her friend again.... she hates me with all her heart as far as I know, the last time we weren't saying hateful things about eachother, we were hugging infront of a soda machine.