Math mini-contest trigonometry problem for Day 5 on D.Buzz for May 2021 😎

Math mini-contest problem for Day 5 on D.Buzz for May 2021 😎

For a triangle DEF whose height is FG and G is on side DE, Manga got arctan (FG/DG) ≈ 1.176, while Minos got arctan (FG/GE) ≈ 0.330. What is the minimum possible area of the triangle if FG is an integer?