When Animate Dead enters, it trigger, returning Sun Titan from your graveyard to the battlefield and attaching Animate Dead to it.
When Sun Titan enters, it triggers, targeting Dance of the Dead.
Holding priority, activate Phyrexian Altar by sacrificing Sun Titan.
Resolve the Sun Titan trigger, returning Dance of the Dead from your graveyard to the battlefield.
When Dance of the Dead enters, it trigger, returning Sun Titan from your graveyard to the battlefield and attaching Dance of the Dead to it.
When Sun Titan enters, it triggers, targeting Animate Dead.
Holding priority, activate Phyrexian Altar by sacrificing Sun Titan.
Resolve the Sun Titan trigger, returning Animate Dead from your graveyard to the battlefield.
Repeat from step 2.
This elegant loop relies on Sun Titan's ability to pull low-cost permanents out of the graveyard whenever it enters the battlefield, creating a perpetual motion machine between your graveyard and the battlefield. By using Phyrexian Altar to sacrifice Sun Titan in response to its own trigger, you free up the sacrifice outlet to generate colored mana while cycling between Animate Dead and Dance of the Dead. Because both enchantments pull Sun Titan right back into play with their entry triggers, the Titan continuously resurrects whichever enchantment you just sacrificed to feed the Altar.