When Ornithopter dies, Nim Deathmantle triggers, choose not to pay for the trigger.
Activate Ashnod's Altar by sacrificing Samwise the Stouthearted, adding ({C} magic symbol) ({C} magic symbol) .
When Samwise the Stouthearted dies, Nim Deathmantle triggers, causing you to pay ({4} magic symbol) to return Samwise the Stouthearted from your graveyard to the battlefield, and attach Nim Deathmantle to it.
When Samwise the Stouthearted enters the battlefield, it triggers, returning Ornithopter from your graveyard to your hand, and causing the Ring to tempt you.