How does Aristarchus of Samos measure distance between earth and sun?

The error in this calculation comes primarily from the poor values for x and θ. The poor value for θ is especially surprising, since Archimedes writes that Aristarchus was the first to determine that the sun and moon had an apparent diameter of half a degree. This would give a value of θ = 0.25, and a corresponding distance to the moon of 80 earth radii, a much better estimate.