Show that the Hadamard gate is equivalent to a 180 degree rotation about the axis defined by $(\vec{e_x} - \vec{e_z}) / \sqrt{2}$ where $\vec{e_x}$ and $\vec{e_z}$ are unit vectors pointing along the x and z axes.

I can visualize that this is true based off the mapping of the computational basis vectors to the Hadamard basis vectors on the bloch sphere but I don't know how to show this mathematically.