Consider Feynman's plate trick.
To get a 1/2 Spin particle to it's original state (put your TV remote on your palm, with your hand in front of you, and your elbow pointing down) you have to rotate it twice.
Keeping the buttons on the remote aimed upwards, turn it to the right and let your elbow rotate out and upwards.
Note when you have the remote facing forwards again, your elbow/arm will be in the opposite state from when you started.
Put the back of the hand holding the remote into the palm of your other hand, with that elbow oriented downwards.
Fits nicely huh, they can share that state because the elbow state is different.
Now continue rotating the remote to the right, under your elbow, and bring your elbow back down to the starting position.
2 Rotations = back to normal.
Can you put the back of the remote hand in the palm of the other hand with both elbows like that?
They can't share that state, neat, but moving on.
How could you rotate something once to reach the starting position?
Grasp the remote, rotate it to the right and flip the buttons so they point down after half a rotation, and then bring it back around forwards again. (NOTE: this is not exact, just helping to consider these concepts)
How could you rotate something halfway and have it arrive at the starting state?
Is there anything you can think of that fits that description?
Does a direction work? the x-axis rotated 180 degrees... is the x axis.
Just something to think about, Gravitons return to the same state when rotated 180 degrees. Spin 2.