What is the Fourier transform of $\frac{x}{\sin(x)}$?

Question

What is the Fourier transform of $\frac{x}{\sin(x)}$? (Not $\frac{\sin(x)}{x}$!)

Answer 1

$x/\sin x$ is not an integrable function, so that the Fourier transform is not defined. Moreover it is not locally integrable, so that the Fourier transform is not defined even as distribution.