USAAAO — 2025 First Round

Two exoplanets, A and B, have circular orbits around the same central star. Suppose that the ascending nodes of the orbits are located at the same ecliptic longitude, defined analogously as the one for the solar system, and that both planets are at that point in the beginning. How long will it take for the planets to have an equal, common ecliptic longitude again, knowing that the inclinations of their orbits are i₁ = 30° and i₂ = 70°, and that their periods are T₁ = 2 yr and T₂ = 1 yr?