Necessary and sufficient condition for reciprocal polynomials to be monogenic

Let $\mathbb{Z}_K$ denote the ring of integers of the number field $K=\mathbb{Q}(θ)$, where $θ$ is a root of a monic irreducible polynomial $f(x)\in\mathbb{Z}[x]$. We say that $f(x)$ is monogenic if $\mathbb{Z}_K=\mathbb{Z}[θ]$. A polynomial $f(x)\in\mathbb{Z}[x]$ is called reciprocal if $f(x)=x^{°(