In one of his videos (https://www.youtube.com/watch?v=HrRMnzANHHs), Matt Parker introduces the following formula for $\pi$ using primes:
$$\left(1-\frac{1}{3}\right)\cdot\left(1+\frac{1}{5}\right)\cdot\left(1-\frac{1}{7}\right)\cdot\left(1-\frac{1}{11}\right)\cdot\left(1+\frac{1}{13}\right)\cdot\left(1+\frac{1}{17}\right)\cdot \ldots=\frac{2}{\pi}$$ Each term is $\left(1+\frac{1}{p}\right)$ if $p \equiv 1 \pmod 4$. Otherwise, the term is $\left(1-\frac{1}{p}\right)$.
Could somebody please explain this formula to me?