Rotation of a Rotation (2)

In the figure below, the black R was rotated by angle alpha around Rotocenter1 (purple). The image of that rotation (the purple R) was then rotated by angle beta around Rotocenter2 (cyan) .
  1. Can a rotation of a rotation be a translation? Adjust the angles of rotation, the rotocenters, and the red vector, so that the red R coincides with the cyan R.
  2. What is the relationship among the angles of rotation in this case? Change the values of all three angles to confirm your conjecture.
  3. Can a rotation of a rotation be a 'do nothing'? Adjust the angles of rotation, the rotocenters, and the red vector, so that the cyan R coincides with the black R.
  4. What is the relationship among the angles of rotation when the composition is a 'do nothing'? Change the values of both angles to confirm your conjecture.