Problem 7. Given angles a, B E [0, 27), prove that the composition of the rotations Ra : R2 + R2 and RB : R2 -> R2 is the rotation Rats : R2 -> R2. Conclude from here that in general an isometry of the plane can not be written as a composition of at most three rotations. Hint. To carry out the proof you will need to use formula (1). Use trig identities whenever possible to make your life easier