Page "Compass and straightedge constructions" Paragraph 33

There is a bijection between the angles that are constructible and the points that are constructible on any constructible circle.

The angles that are constructible form an abelian group under addition modulo 2π ( which corresponds to multiplication of the points on the unit circle viewed as complex numbers ).

The angles that are constructible are exactly those whose tangent ( or equivalently, sine or cosine ) is constructible as a number.

For example the regular heptadecagon is constructible because