Let $\displaystyle f:\mathbb R^2\to\mathbb R$ so that $\displaystyle f(x,y)=(s,t)=\left( x+\dfrac{1}{2}\arctan y,y+\dfrac{1}{2}\arctan x \right)$

Find the linear approximation of $\displaystyle f^{-1}$ on a neighborhood of $\displaystyle (s_0,t_0)=f(0,1).$

Don't worry about the invertibility, that was another question which I solved, but now I need help with this one, I don't get how to solve it.