Results of Shahidi on the analytic continuation of certain L-functions have been used by Serre to obtain partial information on the distribution of Sato-Tate angles of the Ramanujan τ function. Employing the Christoffel numbers associated to the orthogonal polynomials used by Serre we derive upper bounds on the lower density of primes with small angles. We also make effective his lower bounds on the upper density of such primes. Assuming that more analytic information is available, we sharpen similar estimates of Ram Murty, and, using the Christoffel numbers attached to the second order Chebyshev polynomials, derive general bounds on the discrepancy between the empirical angles distribution and the Sato-Tate distribution.