Fast massed air agression
Important note: The strength of this build is the abuse of resource pooling of vespene gas to the Zerg producing mass Mutalisk. Additionally, this can be used in many other scenarios in which a team player will provide the necessary resource for a teammate to construct a large amount of higher tier units at an earlier than usual time frame of the game.
Goal: The goal of this team strategy is to have the Protoss team player construct a Pylon and Forge at the joint choke for both players and provide 3-4 Photon Cannons to prevent any rushes. The Zerg goes for a fast expo, macros up heavily and Techs for a quick mass Mutalisk harassment attack. In addition, the Protoss constructs two Assimilators, and can even go for a fast expo at natural himself to help pool all his gas resource to the Zerg's Mutalisk production. If done correctly, many players will not be ready for such a huge air assault with high mobility.
Execution: Protoss builds first Pylon at joint, creates a Forge and begins constructing 3-4 cannons and roughly stops at around 7-8 (maybe even more), depending on the scouting information of enemy armies. Meanwhile, the Zerg macros up and goes for an extremely fast 15-20 Mutalisk rush in under 6 minutes.
Pros: Allows fast safe expos for the Zerg player and allows constant Drone production to get a powerful economical lead.
Cons: Protoss player is fairly open to Reaper rushes and Stalkers with blink. However, one cannon or so at the main mineral line can prevent this.
This also works well against a dual Protoss team because any tier 1 units before Immortals will get taken care of with the double lines of cannons at the choke, which will buy enough time for a mass Mutalisk attack.
When playing against a Zerg, beware of a (mass) speedling runby. Neither Zerg or Protoss will have any units until pretty late, and you will have 3 (or even 4) bases to defend once the lings are past the cannons. This can be countered by either walling of the choke completely (Protoss will build most of his building there anyways) and/or for Zerg to build a Roach Warren which allows Zerg to quickly build Roaches from his two hatches, if needed. Since the opponent has built lings while you did pure Drones, you can lose quite a lot of Drones and mining time and still be ahead in the macro race.
Zerg player should be perfect with his macro style game play, it is possible to have three Hatcheries timed perfectly with 2 spawn Larvaes so that 15+ Mutalisk start morphing right when fast Spire is finish due to the pooling of mineral/gas resources from the Protoss team player.
MAIN STRATEGY HINT: The strength of this PZ strategy is that the Protoss is effectively establishing a strong line of static defense that can hold a two-player team early to mid team rush while the Zerg can safely macro for a powerful air strike that can ultimately win the game. A map that favors this strategy heavily would be Scorched Haven.
VARIANTS: The Protoss player goes for either a quick Robotics Facility as well to provide Colossi cover or Stargate to have Voidray/Phoenix support with Mutalisk rush.
Transition: Zerg can switch to Brood Lords and the Protoss can support with Stalkers for a deadly combo.