Before revision:  Let } O be a set of k lines passing through the origin . We show=\pi-\alpha_i and \Theta=\min\{\Theta_i:i=1,\ldots,2k\}.
After revision:  Let } O be a set of k lines passing through the origin sorted by slope and let \alpha_i be the aperture angles of the 2k sectors defined by every pair of two consecutive lines. Let \Theta_{i=\pi-\alpha_i and \Theta=\min\{\Theta_i:i=1,\ldots,2k\}.