For what values of $b\in \mathbb R$ is $\pi-b$ rational?

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Just a simple short question. I'm looking for values $b$ such that $\pi-b$ is a rational number. Obviously $\pi$ is such a number, but are there more?

Edit: $b$ is in $\mathbb R$

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Clearly, and almost vacuously $b=\pi+q$ for some rational number $q$. You can easily show that these are the only ones.