Double 3-d Fourier transform

Question

I have a nested Fourier transform as following $$\int\frac{d^3\mathbf{q_1}}{(2\pi)^3}\frac{d^3\mathbf{q_2}}{(2\pi)^3}\frac{1}{\mathbf{q_1}^2\mathbf{q_2}^2(\mathbf{q_1}^2+\mathbf{q_2}^2)}\frac{1}{|\mathbf{q_1}+\mathbf{q_2}|^2}e^{i\mathbf{q_1}\cdot \mathbf{x}}e^{i\mathbf{q_2}\cdot \mathbf{y}}$$ I expect the result to contain $\mathbf{x}\cdot \mathbf{y}$, but I don't know how to do it. Actually I failed to perform the angular integration after I transform the angle between $\mathbf{q_1}$ and $\mathbf{q_2}$ into the one between $\mathbf{x}$ and $\mathbf{y}$. Can anyone show me how to do this properly?