animated modifiers and exporting to fbx

Hello everybody,
I’m quite a noob in Blender, and I’m already encoutering problem for the first animation I ever tried to import from Blender to Unity (fbx format).
The attached file is composed of a circle curve with a ‘Screw’ modifier in order to get an incomplete torus.
I’ve set two keyframes on the angle parameter of the screw modifier in order to make the torus ‘grow’ over time.
As there is no mesh, when I import it to Unity or another soft, the object seems void. But if I apply my ‘Screw’ modifier into Blender, I will loose my animation.
If anyone could give me a clue about how to get what I want it would be great!
(sorry for my english)

loading.blend (475 KB)