Question 74
In the plane rectangular coordinate system, given hyperbola $\Gamma: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ ($a, b \gt 0$), a line with inclination angle $\frac{\pi}{4}$ passes through a vertex of $\Gamma$ and another point $(2, 3)$ on it. Then the eccentricity of $\Gamma$ is ______.