Let G be a finite group of rotations of the plane around the origin, prove that G is cyclic.

Im confused about how to start this (I have not done any group theory in a while)

Thanks for any help

Take the smallest rotation, denoted as g, then there exists a least m such that

As G is a finite group

If m=n then we are done.

If

then there exists an element s.t.

do I then go on to show that if this was the case b must have an inverse and that would be one of the the we have a contradiction?