Formulating a differential equation in polar coordinates

Formulating a differential equation in polar coordinates

A particle is moving with unit speed. Its angular speed is given by this
equation:
$$ \frac{d\phi}{ds}=\frac{2-3\sin^2(\phi - \alpha)}{r\sin(\phi - \alpha)} $$
where $\phi$ is the angle representing the particle's direction of
movement , $\alpha$ and $r$ are the standard angle and distance from the
origin of the particle's position in polar coordinates.
I don't know how to, at least, express the differential equation of the
path the particle takes, so if someone can help, or, if it's not even
possible to formulate it, to give some hints to why it is impossible...
Here, $ds$ is the arc length satisfying
$$ ds=\sqrt{dr^2+r^2 \, d\phi^2} $$
which basically says that the particle is moving with unit speed.