If I have even and periodic signal \$x(t)\$ that has cosine fourier series
$$ x(t)\sim\underbrace{\frac 12}_{a_0}+\sum_{n=1}^{\infty} \underbrace{\left(\frac{6\cos \left(\frac{n\pi }{3}\right)-6\cos \left(\frac{2n\pi }{3}\right)}{n^2 \pi^2} \right)}_{a_n} \cos \left(\frac{n\pi t}{3}\right)$$
because for even function my \$ b_n=0 \$ coefficient vanishes so \$ C_n = a_n \$
If I want to construct amplitude spectra I plot \$a_n\$ with \$n=0, \pm 1\, \pm 2\,...,\$ right? Like this? $$\begin{array}{c|c} n & a_n \\ \hline 0 & 0.5 \\ \hline \pm1 & 0.61 \\ \hline \pm2& 0 \\ \hline \pm3& 0.14 \end{array}$$
But how about the phase spectra. Phase or \$ \theta=\arg(C_n)=\frac{\operatorname{Im(C_n)}}{\operatorname{Re}(C_n)} =\arctan \frac {-b_n}{a_n} \$. But in my case there is no \$b_n\$. Doesn't my fourier serie have phase spectra?