Electric field of two arcs

I have a question about calculating electric field. In the given image you have two line charges which are not infinite. “a” is a radius, and angle “alfa” is given. How to calcululate electric field of point (0,0)? Is it the easiest way to do superposition method? I know how to do this for semi circle, but the gap between charges is a problem. Thanks for the answers. image link: http://i.stack.imgur.com/KoqPZ.png