Use your knowledge of geometry (and/or trigonometry) to show that the
angle α between the worldline of an inertial observer and the lightcone
(drawn in an inertial frame using units in which light rays travel at 45
degrees) is the same as the angle β between that observer’s line of si-
multaneity and the lightcone. (Hint: Many people find it easier to use
trigonometry to solve this problem than to use geometry).