Temple of Atropos

The additional beginning phase will be a lot like your normal beginning phase. During the untap step, permanents will phase in or out as appropriate and you'll untap your tapped permanents. Anything that triggers "at the beginning of your upkeep" or similar will trigger during the upkeep step, and you'll eventually draw a card for your draw step.

The additional beginning phase all happens during the current turn. Any effects that last "until your next turn" or similar won't expire just because you'll go through an additional beginning phase.

After the additional beginning phase, the game proceeds to the ending phase (unless something has added even more phases; see below).

If multiple phases are added to the same point in your turn, the most recently created phase happens first. For example, say the current plane is Temple of Atropos and its ability triggers during your postcombat main phase. Later during that same main phase, another effect gives you an additional combat phase after this main phase. The additional combat will happen first, followed by the additional beginning phase.

Even if you don't attack with any creatures during combat, you'll still get a postcombat main phase and Temple of Atropos's ability will still trigger.

If you somehow have more than two main phases in a turn, each main phase other than the first one is a postcombat main phase, and Temple of Atropos's ability triggers at the beginning of each of them.

The effect of the chaos ability reverses the turn order for players established at the beginning of the game. While the order is reversed, anything that cares about this order (such as determining in what order choices are made) will use the new order.

If the game's turn order is reversed again, it will return to the default order used at the beginning of the game.

If the turn order is reversed during an extra turn, the next non-extra turn will be taken by the next player in turn order from the last player who took a non-extra turn. The order of any pending extra turns isn't affected.

If the turn order is reversed during a two-player game, or during a multiplayer game that only has two players left, it has no noticeable effect on the game.

Reversing the turn order has no effect on the order of steps and phases in each turn. Those steps and phases still happen normally (along with the additional beginning phase).