As you know, Poseidon wields a trident as his weapon. However, I have never heard of any ancient Greeks ever actually using this weapon in battle. Was this actually the case? Did the Greeks have a history of trident-use upon which they based the weapon of the god of the oceans, or did they just give Poseidon a fancy pitchfork and say "fuck it, he can fight with that."
A Trident is a fisherman's spear. That's why it was a symbol of the sea god. The multiple barbed tines help hold the fish on the end of the spear after it's stabbed. It's technically not at all the same as a pitchfork for moving hay. I don't think there was a military purpose to it for the Greeks. The Romans later had gladiators who were given a net and trident to make for an interesting fight, but that's not military and is well after the god's symbol was already part of the culture.