The density function of the random vector \((\xi, \eta, \zeta)\) is

\[ ho(x, y, z)=\left\{\begin{array}{cc} \frac{6}{(1+x+y+z)^{4}} & \text { for } x>0, y>0, z>0 \\ 0 & \text { otherwise } \end{array}\right. \]

Find the distribution of the variable \(\xi+\eta+\zeta\).