Time allotment - time management

The first part of the problem is a very tedious exercise without a computer algebra system. With a CAS, it should be the work of a few minutes. The second part of the problem is the hardest. To save time, it will probably be necessary to hint at the trigonometric identity. the third part of the problem involves finding the maximum value of a function. With a CAS it should be very quick. Estimated time for the whole exercise (if hint is given) about 50 minutes.