Bernstein's Polynomial Theorem

If $g(\theta)$ is a trigonometric Polynomial of degree $m$ satisfying the condition $\vert g(\theta)\vert\leq 1$ where $\theta$ is arbitrary and real, then $g'(\theta)\leq m$.

References

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 5, 1975.