Can a DTFT have a period different of $2\pi$?

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I think almost everything is in the title.

In an exercise, a DTFT is given : $$X(e^{j\Omega}) = \sin(\Omega) + \cos(\Omega/2)$$ The period of this DTFT is $4\pi$. Is that possible? I mean, the definition of the DTFT shows that it is $2\pi$-periodic $$X(e^{j\Omega}) = \sum_{n=-\infty}^\infty x[n]e^{-k\Omega n}.$$

I don't know if a $4\pi$-periodic DTFT has any sense. I'm really confused about this.

Thanks in advance,