Singular Values & the SVD · Challenge problem

Find the condition number $\kappa(C) = \dfrac{\sigma_{\max}}{\sigma_{\min}}$ of the circulant matrix $C = \begin{pmatrix}2 & 1 & 0\\0 & 2 & 1\\1 & 0 & 2\end{pmatrix}$. Give your answer in simplest radical form.