How to fix 'Sparsebundle in Use' errors

Sometimes during an attempted Time Machine backup, you'll encounter this message:
 
Time Machine could not complete the backup. The backup disk image ********.sparsebundle is already in use
 
This problem may be coupled to the Time Machine drive being mounted in the Finder at all times. When Time Machine backs up to network volumes, it first mounts the remote disk image and then unmounts it when the backup is complete. If the disk image does not get properly ejected then this could make Time Machine think the disk image is already in use. Unfortunately users may not be able to eject the mounted image file, and Mac OS X may give an error stating the drive is "in use".
 
Fix:
  1. Ensure no AirDisks are in use (if this is the case, eject them from Finder).
  2. Now open the Airport Utility and choose the Time Capsule device on the list to the left.
  3. Then click the "Manual Setup" button and select "Disks" in the resulting window.
  4. Then click the "Disconnect All Users..." button & quit the utility.
  5. Now try to remount the AirDisks...
  6. Now reattempt the backup
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