A note on trigonometric polynomials for lower bounds of $\zeta(s)$

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in the critical strip, the classical polynomial $3+4\cos(\theta)+\cos(2\theta)$ used by de la Vallée Poussin has since been replaced by more beneficial polynomials with larger degree.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 $\abs{\zeta(\sigma+it)}$ when $\sigma>1$. We show that this polynomial is optimal for this purpose.