NP-hardness of maximal angle computation for the nonnegative orthant

Let $Q\subseteq\mathbb R^n$ be a polyhedral cone, and let ${\rm MA}(P,Q)$ denote the problem of computing the maximal angle between cones $P$ and $Q$. Orthant-restriction conjecture. Computing the maximal angle between $\mathbb R^n_+$ and a polyhedral cone $Q\subseteq\mathbb R^n$ is NP-hard, that is, solving ${\rm MA}(\mathbb R^n_+,Q)$ is NP-hard. The preceding result establishes NP-hardness when the first cone is generated by a subset of the canonical basis; the conjecture asks whether NP-hardness persists when the first cone is the full nonnegative orthant.