Background
I'm looking over this unit circle proof for the formula for $\sin(\alpha + \beta)$ found on Wikipedia: https://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities#Angle_sum_identities
The proof is simple enough, but I'm wondering if the proof holds for, let's say $\alpha \in (0, \frac\pi2), \ \beta = \pi$.
This would make the lines $OP, \ OQ$ colinear, and we wouldn't get all those right triangles to work with, which the proof is heavily dependent on.
Question
Is there a simple re-write of this proof that deals with this special case?