  In this paper, we study the theory of orthogonal trigonometric polynomials
(OTP). We obtain asymptotics of OTP with positive and analytic weight functions
by Riemann-Hilbert approach and find they have relations with orthogonal
polynomials on the unit circle (OPUC). By the relations and the theory of OPUC,
we also get four-terms recurrent formulae, Christoffel-Darboux formula and some
properties of zeros for orthogonal trigonometric polynomials.
