Anatta (say "uh-nut-tah") is usually translated not-self, and it is worth being exact about what the teaching actually claims. It does not say you don't exist. In an early sermon at Isipatana, the Buddha examined the body, feelings, perceptions, thoughts, and awareness itself, one by one, and found that none of them could be a fixed, controllable self, because none of them could be commanded not to change or suffer. Later teachers were careful to frame this as neither "there is a self" nor "there is no self," calling both extremes a wrong turn. The useful move isn't a metaphysical verdict, it's a question: is this feeling, this mood, this label, really me, or mine, or just passing through. Try it once today on an ordinary irritation. Instead of "I'm annoyed," notice: irritation arose. See what shifts when you drop the ownership, not the experience.
To hold either that there is a self or that there is no self is to fall into extreme forms of wrong view that make the path of Buddhist practice impossible.
Thanissaro Bhikkhu, "No-self or Not-self?"