An ellipse has semi-major axis $a=5$ and semi-minor axis $b=4$. A point $P$ moves on the ellipse such that its eccentric angle $\theta$ changes at a constant rate $\frac{d\theta}{dt} = 2$. What is the magnitude of the velocity vector $\vec{v} = (\frac{dx}{dt}, \frac{dy}{dt})$ when $\theta = \frac{\pi}{4}$?