Let's start with some poetry by high school trig students:
one by Elizabeth Palmieri
and
one by Erin Stanley
Good books, etc. for reference:

Resources on the Web
Web searches for "trig identities" at google.com and at msn.com lead to the following links (and many others):

Building Blocks:
A fundamental set of relationships and identities

Application:
CMJ problem 709
Basically, this problem asked for solutions to the equations
(a) p/4 = arctan(q) + arctan(x) (b) p/4 = arctan(q) + 2arctan(x) 