  Using Stein's method for the Beta distributions and a recent technique by
Goldstein and Reinert of comparing the Stein characterization of the target
distribution with that of the approximating distribution we prove a rate of
convergence in the classical arcsine law, which states that the distribution of
the relative time spent positive by a symmetric random walk on $\Z$ converges
weakly to the arcsine distribution on $[0,1]$.
