What Is $\theta$?

The following formula is for the force, $F$ on a sphere moving through a fluid of density, $\rho$ at a velocity of $v$ and a spin about a axis, $\omega$, 

$F=\pi^2r^3\rho\omega\times v=\pi^2r^3\rho\omega v cos(\theta)$

from the book "The Math Behind..." by Colin Beveridge, Cassell,  Octopus Publishing Group Ltd.

For $\theta=0$, the spiral flattens out and the particle is just in circular motion.  For a spin axis through the center of the particle, $r=a_{\psi}$; $r$ is the size of the particle.

Since,  $cos(\theta=0)=1$,  $F=F_{max}=\pi^2r^3\rho\omega v$

If $v=c$ and $v=r\omega=c$

$F_{max}=\pi^2r^3.\rho.\cfrac{c^2}{r}=\pi^2r^2.c^2.\rho$

And if this force is the drag force, which is proportional to velocity squared,

$F_{drag}=F_{max}=k.c^2=\pi^2r^2.c^2.\rho$

$k=\pi^2r^2.\rho$

And in general, $\theta\ne0$, the spin axis is not through the center of the particle, and the spiral stretches out,

$k=\pi^2r^2.\rho.cos(\theta)$

where $\pi r^2.\rho$ is the mass per unit length in direction perpendicular to the area $\pi r^2$.  This value multiplied by $v$, $\pi r^2.\rho.|v|$ is the mass of the fluid displaced by the particle of radius $r$ with velocity $v$ in one unit second.
 
$k=\pi.cos(\theta).m_{fluid,\,v}$

$m_{fluid,\,v}=\pi r^2.\rho.|v|$

What is $\theta$?