Well you have to watch the video carefully to understand what I mean. He doesn't explain how he got -theta. Any variable could have been used, why that though? Theta had already been used at the start of the video. If he used it again, he should have explained why. You can't just use theta for two different sized angles. He must explain how the second theta got there.
You can close the discussion. He has to be right not necessarily because theta is a time variable but because of a standard geometrical rule. No matter where the inner circle is, if you strike a line going through the starting point (on its edge) and its radius, which will inevitably intersect one of the lines which forms the angle theta on the large circle, the angle theta will be produced. What you essentially get is two parallel lines intersecting another line going through the radius of the large circle and the radius of the smaller circle. This is what the tutor didn't explain. I knew it had to be the reason why, but it only became obvious after using a pair of compasses to construct the proof.
I have to think of two points on the smaller circle. The starting point which never moves, and the new point which can change.