Proof of Zeta (2) Function: Short & Concise

[XtremePhysX]

Homework Statement

Find the shortest way possible to prove:

Homework Equations

\zeta (2)=\frac{\pi^{2}}{6}

The Attempt at a Solution

I trying doing sinx < x < tanx if u know what I mean but it took me 6 pages.
I want a prove that is short and concise.
Also, can you guys please show full working?

 

[micromass]

Is this really homework?

May I know what your mathematical background is?? I ask this because the shortest possible proofs will require quite some mathematical knowledge such as Fourier series or complex analysis.

 

[XtremePhysX]

Is this really homework?

May I know what your mathematical background is?? I ask this because the shortest possible proofs will require quite some mathematical knowledge such as Fourier series or complex analysis.

Yes, I just want the shortest possible prove, a really concise prove.
Show me the prove, and leave the rest for me, I'll understand it.

 

[voko]

http://en.wikipedia.org/wiki/Basel_problem