How to rotate these sticks evenly so that they roughly stay in place. I tried to use the array modifier and make them separate objects, and also somehow rotate them in relation to the 3D cursor, but it didn't help.
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It seems to work fine:
Do it again.
If you need to animate the sticks, first parent the initial stick to an empty, then duplicate both the empty and the stick, move and rotate, and you'll animate each stick: