Is there a simple relationship between angle of attack and lift coefficient? Is there an equation relating AoA to lift coefficient?

I have been searching for a while: there are plenty of discussions about the relation between AoA and Lift, but few of them give an equation relating them.

I know that for small AoA, the relation is linear, but is there an equation that can model the relation accurately for large AoA as well? (so that we can see at what AoA stall occurs)

I am not looking for a very complicated equation. Can anyone just give me a simple model that is easy to understand?

(Of course, if it has to be complicated, then please give me a complicated equation)
In the post-stall regime, airflow around the wing can be modelled as an elastic collision with the wing's lower surface, like a tennis ball striking a flat plate at an angle. Lift and drag are thus:

$$c_L = sin(2\alpha)$$
$$c_D = 1-cos(2\alpha)$$

I superimposed those (blue line) with measured data for a symmetric NACA-0015 airfoil and it matches fairly well. I don't know how well it works for cambered airfoils.