See Eq. (7.5.2), or equivalently Eq. (12.6.6).
See also my solution for Problem (7.11.2).
The Kronecker delta function is defined in
Eq. (3.9.4)
See Eq. (8.11.13), as well as my notes on the Dirac Delta
function Section (on March 24th).
See Eqs. (12.7.1), (12.7.6), and (12.8.1).
Alternatively, you may start from the identity, which can be viewed
as a Fourier Sine series expansion for sin3x, and get to the Complex
Fourier series (with a finite number of terms) using Eq. (7.7.1).
See Eq. (8.5.11), as well as Example 3 of Section 8.5.
See Eqs. (8.6.18) and (8.6.23). See also Problem 8.6.36, which
is a Homework problem.