You don't need to do that simultaneously, it's also possible to do it successively.
It is possible to rotate an object numerically using Object -> Transform.
With this, you can first:
- duplicate one of your objects twice, so you have three identical pieces, with the same rotation
- rotate the two copies by the necessary angles
- then move them until the corners snap to each other, with the correct snap option enabled (the one for cusp corners is the correct one, I think).