I'm studying the Riemann $\zeta$-function, and I'm now finding out that, apparently, whenever $\rho$ is a zero of $\zeta$, $\overline{\rho}$ is also one. This follows easily from the identity $\zeta(\overline{s}) = \overline{\zeta(s)}$, which I saw on wikipedia and here: Is Riemann Zeta Function symmetrical about the real axis?.
However, how does one prove this identity?