Currently studying analytic number theory and was baffled by the following integral representation of $\zeta(n)$
$$\zeta(n) = \dfrac{2}{1 - 2^{1 - n}}\sin\left(\dfrac{\pi n}{2}\right)\int_0^\infty \dfrac{x^{-2n}}{\pi x}(1 - \pi x^2\csc[\pi x^2])dx$$
However there's no proof for this provided in the text. I am struggling on proving the same.
Any help or hints would be highly appreciated.
Thanks.