Partial Fractions Expansion of Cotangent/Proof 2

Proof
From the Euler Formula for Sine Function:
 * $\ds \sin x = x \prod_{n \mathop = 1}^\infty \paren {1 - \frac {x^2} {n^2 \pi^2} }$

Taking the logarithm of both sides:

and differentiating $x$:

Hence the result.