Note that when b = 1, hence, coss = ±1= coss'_i, when positive s = 0º (0) = s'_i and when negative s = 180º (p) = s'_i.  Also when b is zero, coss  = 0 = coss'_i and thus when dp and dip' are positive s = 90º (½p) = s'_i (and cscs = 1 = cscs'_i), while when dp and dip' are negative s = 270º (3p/2) = s'_i (and cscs = -1= cscs_i).  (The range of the cosecants in both equation [7] and [10] is ±¥)