Line Integral on Sphere (Part 2)

Consider the following curve, where the coordinates of each point on the curve are $(x,y,z)$ :

$x = \cos \theta \, \sin \phi \\ y = \sin \theta \, \sin \phi \\ z = \cos \phi \\ \theta = \alpha \\ \phi = \frac{\pi}{2} - \alpha \\ 0 \leq \alpha \leq \frac{\pi}{2}$

There is also a vector field present at all points in space:

$\vec{F} = (F_x,F_y,F_z) = (x y,y z,z x)$

What is the absolute value of the line integral of the vector field over the curve?

$\Big | \int_C \vec{F} \cdot \vec{d \ell} \, \Big | = ?$