  Cotangent sums are associated to the zeros of the Estermann zeta function.
They have also proven to be of importance in the Nyman-Beurling criterion for
the Riemann Hypothesis. The main result of the paper is the proof of the
existence of a unique positive measure {\mu} on $\mathbb{R}$, with respect to
which certain normalized cotangent sums are equidistributed. Improvements as
well as further generalizations of asymptotic formulas regarding the relevant
cotangent sums are obtained. We also prove an asymptotic formula for a more
general cotangent sum as well as asymptotic results for the moments of the
cotangent sums under consideration. We also give an estimate for the rate of
growth of the moments of order 2k, as a function of k.
