We use the Kobayashi-Hitchin correspondence for parabolic bundles to reprove the results of Troyanov [Trans. Amer. Math. Soc. 324 (1991), pp. 793-821] and Luo-Tian [Proc. Amer. Math. Soc. 116 (1992), pp. 1119-1129] regarding existence and uniqueness of conformal spherical metrics on the Riemann sphere with prescribed cone angles in the interval (0, 2π) at a given configuration of three or more points.