Orthogonality & Least Squares · Superchallenge problem

The data $y_k = k$ at the six times $k = 0, 1, 2, 3, 4, 5$ are fitted by least squares with a model $y = a + b\cos\dfrac{\pi k}{3} + c\sin\dfrac{\pi k}{3}$. Find the minimum possible sum of squared residuals.