(Originais Teachy 2023) - Question Very Hard of Mathematics

Consider a lighthouse located on an island that emits a beam of light that varies its direction over time following a trigonometric pattern. If at a given moment the lighthouse is directed towards a point P in the water, and the light line forms an angle of 75 degrees with the surface of the water, determine the point Q that will receive the light reflected on the surface of the water if it forms an angle of 15 degrees with the incident line. Then, determine point R on the light line that starts from the lighthouse and forms an angle of 22.5 degrees with the light line incident on point Q. To do this, use sines and cosines of the given angles, assuming that light travels in a straight line and that there is no refraction. Explain the reasoning step by step, highlighting the use of trigonometric relationships for each step of the calculation.