Finding the Fourier Transform of $\frac{sinx}{x^2}$

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I have been given the fourier transform for $f\left(x\right) = 1/x$ as

$\hat f = -iπ \,{\rm sgn}\left(x\right)$

I need to find the Fourier Transform of $\frac{\sin x}{x^2}$ using convolution somehow

My attempt was to use $f\left(x\right) = 1/x$ and find some $g\left(x\right)$ such that $f*g\left(x\right)$ would be $\frac{\sin x}{x^2}$ but I cannot find such a $g\left(x\right)$