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You can use a Timeline with five Keyframes to record the object's rotation at five points and a Signal Manipulator to scale the value of your variable from -180 -> +180 to 0.0 -> 1.0. Here are the steps to do that:
1. Enable the grid snap guide.
2. Create a Timeline.
3. Open the Timeline's canvas.
4. Set the left edge of the Timeline to slightly less than -1 second.
5. Set the right edge of the Timeline to slightly more than +1 second.
6. Zoom the Timeline canvas in until you can see individual frames.
7. Adjust the left trim of the Timeline to exactly -30 frames.
8. Adjust the right trim of the Timeline to exactly +30 frames.
9. Create and start recording a Keyframe at the centre of the Timeline (0 frames).
10. Press L2 while hovering over your object to record its current position.
11. Stop recording.
12. Narrow the Keyframe until it occupies less than 1 frame.
13. Open the Keyframe's tweak menu.
14. Set the Keyframe's blend to linear.
15. Turn off the Keyframe's smoothing.
16. Close the Keyframe's tweak menu.
17. Create a clone of the Keyframe at -15 frames on the Timeline.
18. Re-record the second Keyframe.
19. Rotate the object counterclockwise about its axis by 90 degrees.
20. Stop recording.
21. Narrow the second Keyframe until it occupies less than 1 frame.
22. Create a clone of the second Keyframe at -30 frames on the Timeline.
23. Re-record the third Keyframe.
24. Rotate the object counterclockwise about its axis by a further 90 degrees.
25. Stop recording.
26. Narrow the third Keyframe until it occupies less than 1 frame.
27. Create a clone of the first Keyframe at +15 frames on the Timeline.
28. Re-record the fourth Keyframe.
29. Rotate the object clockwise about its axis by 90 degrees.
30. Stop recording.
31. Narrow the fourth Keyframe until it occupies less than 1 frame.
32. Create a clone of the fourth Keyframe at +30 frames on the Timeline.
33. Re-record the fifth Keyframe.
34. Rotate the object clockwise about its axis by a further 90 degrees.
35. Stop recording.
36. Narrow the fifth Keyframe until it occupies less than 1 frame.
37. Create a Signal Manipulator.
38. Open the Signal Manipulator's tweak menu.
39. Set the Signal Manipulator's remap type to custom remap.
40. Set the Signal Manipulator's input upper threshold to +180.
41. Set the Signal Manipulator's input lower threshold to -180.
42. Wire the Signal Manipulator's signal output to the Timeline's playhead input.
43. Wire the value of your variable - either from the Variable gadget itself or from a Variable Manipulator gadget with the get operation - to the signal input of the Signal Manipulator.