Building a function from 3 given properties

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Is there a real function $f$ / algebraic expression, such that

  • $f(-3) = 1$
  • $f(3) = 1$
  • $f(x) = - f(x)$ for all $-3 < x < 3$

I was able to construct some $f$ with Fourier analysis and complex arguments but this wasn't what I was looking for. :(