u/Dry-Comfortable8410

Would love help with this: suppose a chord is drawn inside a circle. A second chord is drawn at angle theta to the first one. Suppose this process repeats (i.e. a third chord drawn again at angle theta to the second chord..) itself until the initial point from which the first chord was originally drawn is reached again. Suppose further that all of the chords are the same length. Prove either that the first point is always reached again after a finite sequence for any angle theta or, if not, show the conditions under which that does not happen. Does it matter whether the angle is rational or not? Why or why not?