How do I reclaim 36 GB of missing space on my iPhone? I have a 64GB iPhone 5S with iOS 8.4, but I'm only able to access 28 GB of space.

iTunes reports a capacity of 55.92GB, but in the usage graph at the bottom of the summary page, I see:


13.61 GB Free
1.58 GB Other
1.09 GB Documents &amp; Data
5.13 GB Apps
248.3 MB Photos
6.34 GB Audio


The Setting->Usage->Storage app says:


Used: 42.9 GB
Available 13.0 GB


I've tried rebooting and updating the OS from 8.3 to 8.4. 

I'm hoping to avoid a solution that involves wiping the phone and resetting it. Is there anything else I can do to reclaim my missing 36 GB of space?
You said you don't want to wipe the phone and reset it, but what about restoring it from a backup? During an iCloud restore, iOS re-downloads most of what it needs from Apple’s servers, so the process might reclaim your lost space, since iOS wouldn’t assign it to anything that isn't actually using it. After the restore, your phone would be returned to the same state you left it in.