The Best-Laid Plans
Go into the palace and get ready for a hard fight. When you will try to enter the gate it will close, and Locust will start to attack you from above.
Hide behind a column and start eliminating your enemies. In the centre of the room there is a button, if you step on it some additional covers will appear. Kill every single enemy, go outside and turn right. Find another entrance to the palace.
After a while you will arrive at an elevator. Don't use it just yet. A little bit further, near the grated passage you will find the Locust Invasion Map. It's hardly visible, so don't miss it. Now backtrack to the elevator and activate it. Go to the lower parts of the palace.
You will find yourself in a long corridor, with locked beasts on each side. Get past them, and at the exit you will have to choose which road you will take.
If you choose the higher road, go up the stairs and start shooting at the Locust fighting below you.
Follow the corridor till the end and you will find the Trinity of Worms Artifact. Now go back and open the gate for the squad.
If you choose the lower road, enter the room and kill the Locust.
Wait for the gate to open and enter the big door in the centre.
Exit through the newly opened gate. In front of you, between two columns you should see an obelisk. Shoot its higher part and you will discover that there is a toaster beneath the layer of rock. Approach the device, press X and a while to hear a funny comment. It's an Easter Egg which the creators hide in the game to please the curious seekers.
Slowly go down the spiral stairs. You will be attacked by guards and Therons with crossbows, so be careful and don't charge.