USAAAO — 2023 First Round

Consider a hypothetical planet orbiting the Sun with an obliquity angle i (angle between the axis of rotation and the normal to the orbital plane). Assume that a year is much longer than a day for this planet. Define a tropical region in the planet as one where the Sun reaches the zenith at some time in its revolution period. Define a frigid region in the planet as one where there is a day when the Sun never rises. What is the minimum value of i for which there is a location on the planet which is both tropical and frigid?