> Now, the line EC is perpendicular to AB, and the line BC is perpendicular is AC, so the angle ∠BCE is the same as the angle ∠CAD which we called α.

I'm hoping that's a typo, and should be:

> Now, the line EC is perpendicular to AD, and...

(Edit: although I vaguely recall in school doing that bit as the sum of the angles around point C)