A line passing through the point of intersection of $x + y = 4$ and $x - y = 2$ makes an angle $\tan^{-1}\left(\frac{3}{4}\right)$ with the $X$-axis. It intersects the parabola $y^2 = 4(x - 3)$ at points $(x_1, y_1)$ and $(x_2, y_2)$, respectively. Then $|x_1 - x_2|$ is equal to