I don't quite see how the following hold and would appreciate an explanation:
(1) The Fourier coefficients of $cos(\frac{6\pi n}{N})$ are $\delta[k-3]+\delta[k+3]$
(2) $\sum_{n=0}^{N-1}\delta[n]e^{-\frac{j2\pi kn}{N}} = 1$
Where $\delta[n]$ is the discrete dirac function.
Have a look at this link http://www.thefouriertransform.com/pairs/sinusoids.phpIt might help