When Arid Archway enters the battlefield, it, Emeria Angel, and Kodama of the East Tree trigger.
Resolve the Kodama of the East Tree trigger, choosing not to put anything from your hand onto the battlefield.
Resolve the Arid Archway trigger, returning it from the battlefield to your hand.
Resolve the Emeria Angel trigger, creating a token.
When the token enters the battlefield, Kodama triggers, putting Arid Archway from your hand onto the battlefield.
When Arid Archway enters the battlefield, it and Emeria Angel trigger.
Repeat from step 4.
This clever loop relies on Kodama of the East Tree as your engine, letting you bypass mana costs whenever a permanent enters your battlefield. By dropping Arid Archway, its self-bounce trigger allows you to return it directly to your hand just in time to be recast. Meanwhile, Emeria Angel capitalizes on every single iteration by generating a Bird token upon landfall. That token's entry triggers Kodama of the East Tree all over again, cheating Arid Archway right back into play to sustain the chain indefinitely.