Well, you shouldn't actually, it's nothing for you to put much thought in, you had nothing to do with it, and can't change it. If you're grandfather was a rapist, it wouldn't make you a rapist right? There is no reason to feel ashamed of what your race have done in the past.
And hey, if that's what you're worried about, evolution is taking revenge on the white race, mostly because it's us who sit on all the money and technology in the world and don't want to share, it's making us lazy, unhealthy and just genetically bad. Give evolution a few thousand years and I guess there won't be a pure white race left, or they will atleast have become a minority. It's large scale karma, if you go around screwing everyone over you will end up badly, person or race, just take the ancient romans as an example, they took over half the world, but their greed led to their downfall.
So you can do three things, 1. don't care or worry about it 2. be depressed over it for the rest of your life 3. be aware of it, and try and be a better person, charity? Anything. However, you don't want to be depressed about it, that's your problem right? So just live with it, get over it I say! How? Well take up a new hobby, pursue love, I recommend painting, helps me when I'm feeling down. And you're a girl? Maybe just give it a cry? Just express your emotions in some way, paint, write or do, whatever you do, just make sure you get over it, get past the bad thoughts and emotions.