  The sum $c_0(1/k)=-\sum_{m=1}^{k-1}(m/k)\cot(m{\pi}/k)$ is related to the
Estermann zeta function. A recent paper computes the first two terms of the
large-$k$ asymptotic expansion of $c_0(1/k)$. Using the Poisson summation
formula for finite sums, we find three additional terms.
