Find the CDF of $Z=\{X_1+X_2, X_1<X_3\}$

Question

Let $X_1, X_2$ and $X_3$ be three independent exponential random variables. The PDF and CDF of $X_i$ with parameter $\beta_i$ are $$ f_{X_i}(x_i)=\beta_i e^{-\beta_i x_i} $$

$$ F_{X_i}(x_i)=1-e^{-\beta_i x_i} $$

What is the CDF of random variable $Z$ define the sum of $X_1$ and $X_2$ where $X_1$ is less then $X_3$. $$Z=\{X_1+X_2, X_1<X_3\}$$.

Thanks.