I'm curious to know if there exists a way to rationalize this:

$\displaystyle \frac {2}{\pi}$

But without dividing it by 1 or some number.

I always knew about rationalizing fractions with square roots, cube roots, etc, but that question never crossed my mind.

Is there a way to rationalize that fraction? If not, is there a way to prove that you can't?

Thank you