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Would an Eldritch Raider that is able to cast a 3rd level arcane spell thanks to Major Eldritch Magic get an extra spell from Improved Eldritch Heritage: Arcane? It says you must be able to cast a spell from that level, and you are!
No. because those are spell-like abilities.
You gain an extra sorcerer spell of that level, yes. Pity you have no sorcerer spell slots to cast it with.