Proof that ζ(n) = π^n divided by an integer for even n

[nicksauce]

It seems like zeta(n) = (pi)^n / (some number), for even integers n. Can anyone point me to a proof of this?

 

[dalle]

you can find the formula in chapter 4.5 The Cotangent of "On Euler footsteps. Uppsala Lectures on Calculus" by Evgeny Shchepin.
you can download it at
http://www.pdmi.ras.ru/~olegviro/Shchepin/index.html
or
http://at.yorku.ca/i/a/a/z/20.htm