You have enough mana available each turn to cast the extra turn spell and enough mana each extra turn to cast
Ardent Elementalist.
You have not cast a spell using
Kotis.
Steps
Cast the extra turn spell by paying its mana cost, causing you to take an extra turn after this one.
Move to your extra turn.
Activate
Altar of Dementia by sacrificing
Ardent Elementalist, causing you to mill cards equal to
Ardent Elementalist's power.
Cast
Ardent Elementalist from your graveyard by paying its mana cost and exiling three other cards from your graveyard, ensuring not to exile the extra turn spell.
When
Ardent Elementalist enters the battlefield, it triggers, returning the extra turn spell from your graveyard to your hand.