\(X\) and \(Y\) are independent and identically Cauchy distributed with parameters \(\lambda=1\) and \(\mu=0\), i.e. they have densities

\[f_{X}(x)=\frac{1}{\pi} \frac{1}{1+x^{2}}, \quad f_{Y}(y)=\frac{1}{\pi} \frac{1}{1+y^{2}}, \quad-\infty

Verify that the sum \(Z=X+Y\) has a Cauchy distribution as well.