Monte Carlo Method for View Factor Calculation.

I wrote a code for disk to disk view factor via the Monte Carlo Method. However, right now I need to write another code for view factor between disk to sphere. They are coaxial and the sphere's center is $1\mathrm{.}7$m above the disk center. Sphere has a $0\mathrm{.}42$m radius $($In other words, the closest point of the sphere to the disk is $1\mathrm{.}28$m above the disk and the farest point is $2\mathrm{.}12$m above the disk$).$ The radius of the disk is $0\mathrm{.}85.$ Now, for the $45\backslash$deg part of the disk $($not the whole$),$ and using the Monte Carlo method variables that I used previously and you can find it attached in the picture, please write a Python code for the view factor between disk $(45\backslash$deg part$)$ to the sphere.