Can’t create a new partition on an external drive’s free space

I have a USB2, 500GB external hard drive that I use for Time Machine backups. In order to test something, I created a new partition in the drive, roughly 30GB in size. Once I was done with my tests, I wanted to delete the partition and merge the free space back to the original, larger partition.
When I deleted the small test partition with Disk Utility, I encountered an error. A pop-up indicated that I should try to repair the disk, and that I did. Afterwards, the old partition appears as free space, but when I try to create a new partition on that free space (and it doesn't matter which kind of file system), I hit "apply" and the partition isn't created. When I try to move to a different tab in Disk Utility, it warns me that there are unsaved changes.

This is my diskutil output:

Asafs-MacBook-Pro:~ asafchelouche$ diskutil list
/dev/disk0
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *251.0 GB   disk0
   1:                        EFI EFI                     209.7 MB   disk0s1
   2:          Apple_CoreStorage                         250.1 GB   disk0s2
   3:                 Apple_Boot Recovery HD             650.0 MB   disk0s3
/dev/disk1
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:                  Apple_HFS Macintosh HD           *249.8 GB   disk1
                             Logical Volume on disk0s2
                             <intentionally left out>
                             Unencrypted
/dev/disk2
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *500.1 GB   disk2
   1:                        EFI EFI                     209.7 MB   disk2s1
   2:          Apple_CoreStorage                         464.7 GB   disk2s2
   3:                 Apple_Boot Boot OS X               134.2 MB   disk2s3
/dev/disk3
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:                  Apple_HFS Asaf's Time Machine... *464.4 GB   disk3
                             Logical Volume on disk2s2
                             267758BA-8C0B-4710-B626-1909F9126576
                             Unlocked Encrypted

Note: the free space is right after the currently functioning partition, and it spans all the way to the disk's end.

What should I do in order to create a partition on the hard drive, so I could merge it back into the larger partition?

EDIT:
I've followed this post, but to no avail: when trying to execute the following command:

sudo gpt add -b 908317520 -i 4 -s 68390024 -t 48465300-0000-11AA-AA11-00306543ECAC disk2

I get this error message: gpt add: unable to open device 'disk2': Resource busy. I guess this is the same error that is returned to Disk Utility's GUI when I tried to create a new partition. Any thought on how to "un-busy" the device? (I executed diskutil umountDisk /dev/disk2 in advance, and the requested partition size is divisible by 8)

P.S.
This is the output for sudo gpt -r show /dev/disk2:

      start       size  index  contents
          0          1         PMBR
          1          1         Pri GPT header
          2         32         Pri GPT table
         34          6         
         40     409600      1  GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B
     409640  907645736      2  GPT part - 53746F72-6167-11AA-AA11-00306543ECAC
  908055376     262144      3  GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC
  908317520   68390031         
  976707551         32         Sec GPT table
  976707583          1         Sec GPT header