Singular Values & the SVD · Superchallenge problem

Let $C$ be the $8\times 8$ matrix with rows and columns numbered $0, 1, \ldots, 7$ and entries $c_{jk} = \cos\dfrac{2\pi jk}{8}$ (the real part of the $8$-point Fourier matrix). Find the sum of its singular values. Give your answer in simplest radical form.