How to catch a cheater?

So this is gonna sound pretty bad, but I've been in a serious relationship with this girl. We moved in together, we do everything together but as of recently she has been acting like a cheater. The things she is doing are obviously texting all the time and lies about it. She will go out but never say where or who she is seeing or even when she will be home. All the signs are there and when I go to talk to her about it she gets mad every time and we argue eventually it's all my fault. After all this happens she backs off for a few days then is back to the same behavior. 1) yes I know I need to drop her like a ton of bricks. However every time I try she claws her way back in my life and everything repeats. What do cheaters gain from staying in a relationship that their not happy in? And how can I catch her?
How to catch a cheater?
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