Community, with Herculean effort, decided to elementary task.
The problem is different.
A). Maple, Mathematica ... do not have good trigonometric routines.
2). It is necessary not to go to marasm. Namely, combine the capabilities of Maple and its own brain.
3). The main thing. On the planet there are few people who care about trigonometry.

The most popular at the moment nontrivial trigonometric problems in Maple 16: http://webmath.narod.ru/do/c1.html

Trigonometry - it is the Sahara desert for mathematical systems.
Typically, in this case, I rely on myself.