Yeah that gay brigade was formed
in Thebes. It was the Thebans who utterly defeated Sparta in the IVth century ending its power and liberating the Mesenian Helots, although that was due to superior tactics.
I hadn't heard before that Spartans wore little armour, as far as I know Spartan hoplites were as heavily armed as the rest of the Greek ones, armour did matter for their tactics. Actually it was Athens the first to use with good success light assault infantry in the war against Sparta, although those toops were foreing not Athenian. Anyway the film exaggerates Spartan war proficiency compared to other Greeks', or rather exaggerates other Greeks' incompetence. Not only the Spartans were finally defeated, beforehand they were regarded as very good because of their education and exclusive dedication, but not invincible at all, as experience repeatedly proved.