Look at the diagram
I know $\theta$, D and ratio of a/b (say k). I am trying to find out $\alpha$. Is this possible? I couldn't crack it. (I only know the ratio of a to b, and I don't know the c as well)
UPDATE I think I have found a solution. Look at this.
ratio of these two => (a+b)/a=2D/(2D-x)
We know a/b and D. We can find x. Since we know $\theta$, we can find $\alpha$.
I am starting a bounty for somebody who can prove this solution wrong. If it is correct, it is mine to keep.
Ok.. My bad.. I am overall decent guy but fall on my face on this one.