Please submit the solution to this problem via e-mail to email@example.com. The next hint for the Problem 3 will be published at 13:00 GMT, 20th February 2022, together with the next updates of the intermediate results.
It is convenient to consider the following 4-momenta: (a) of the rocket at the moment when the direction of the engine was changed; (b) of all the photons sent in the initial direction (i.e. until the direction of the engine was changed); (c) of all the photons emitted after the direction was changed. With all the relativistic invariants based on these three 4-momenta (cf. Hint 1), the angle \alpha can be conveniently expressed in terms of a parameter, for instance in terms of the time-component of the 4-momentum (b), as measured in the frame of the rocket at the moment when the direction of the engine was changed.