An analytical solution for the differential group delay of a fiber spun according to a triangular function is derived from concatenation of Jones matrices for a fiber length equal to N x T, where T is the spinning period and N is an integer. This solution holds for any value of linear deterministic birefringence delta beta of amplitude A and period T of the triangular spinning function. We use the solution to emphasize the effect of birefringence on the efficiency of the spinning function.