This section of the book "Trigonometry 1" contains additional material and exercises for enthusiasts. Like "Trigonometry 1" itself, none of the exercises in this section require calculus, complex numbers or power series. The exercises are generally harder than in the main text. None of them are part of the core material, but some of the exercises and extensions here will be of interest and fun for some students.
The 'for Enthusiasts' sections are to interest and engage the student who is racing ahead. They aren't a general dumping ground for off-syllabus topics. They are to help bright students who would otherwise be getting bored. These students may also be neglecting to practice their trig skills, so the idea is that the trig for enthusiasts will get them thinking and practising again.
We also have book 2 on the relations between circles and triangles. This book goes well off-syllabus, at least as far as most modern trig syllabi are concerned, and is intended to help these students too. Fluency with the material in it is, for example, relevant for maths contests.