  In this work, some theorems are established for orthogonal trigonometric
polynomials (OTP) including Favard, Baxter, Geronimus, Rakhmanov, Szeg\"o and
the strong Szeg\"o theorems which are important in the theory of orthogonal
polynomials on the unit circle (OPUC). All these results are based on the
mutual representation theorem of OPUC and OTP which deduced by a
Riemann-Hilbert problem simultaneously characterizing them. In addition,
Szeg\"o recursions, four-term recurrences and some new identities for OPUC and
OTP are also obtained by using their Riemann-Hilbert characterizations
respectively.
