Let \(\xi\) and \(\zeta\) be independent and let them have the density functions

\[ p_{\xi}(x)=p_{\zeta}(x)= \begin{cases}0 & \text { for } x \leqslant 0 \\ \lambda e^{-\lambda x} & \text { for } x>0\end{cases} \]

Prove that the relation \(\eta=\frac{\xi}{\xi+\zeta}\) is distributed uniformly on the interval \((0,1)\).