A note on trigonometric polynomials for lower bounds of ζ(s)

Non-negative trigonometric polynomials satisfying certain properties are employed when studying a number of aspects of the Riemann zeta function. When establishing zero-free regions in the critical strip, the classical polynomial 3+4cos(θ)+cos(2θ) used by de la Vall\'ee Poussin has since been replaced by more beneficial polynomials with larger degree. The classical polynomial was also employed by Titchmarsh to provide a lower bound on |ζ(σ+it)| when σ>1. We show that this polynomial is optimal for this purpose.