In 2010, Hiriart-Urruty and Seeger posed the problem of finding the maximal possible angle \(\theta _n\) between two copositive matrices of order n. They proved that \(\theta _2=\frac{3}{4}\pi \) . In this paper, we study the maximal angle between two copositive matrices of order 3. We show that \(\theta _3=\frac{3}{4}\pi \) and give all possible pairs of matrices achieving this maximal angle. The proof is based on case analysis and uses optimization and basic linear algebra techniques.
