Phase of a real number
Or $2\pi$, or $3\pi$, or any integer multiple of $\pi$.  Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.

"Phase of a real number" is a little bit of a misleading label.  What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.

Your question is equivalent to "For what values of arg(z) is z a real number?"

If that is meaningless to you, I suggest you start by reading two blog articles of mine:

The Exponential Nature of the Complex Unit Circle

And the newest:

Angle Addition Formulas from Euler's Formula

There are of course many other searches.  Your terms should be "complex plane real values" for a start.

This is essential foundation material for a lot of DSP concepts.