Install zerofree
edit your fstab, set your root drive to RO like
/dev/vda1 / ext2 ro 0 1
Halt your system
# halt -p
Start your system into the grub menu, then select rescue mode, then drop to root shell
Run zerofree like
# zerofree /dev/vda1
Remount your root drive RW
# mount -o remount,rw /dev/vda1
Re-edit your fstab to his origins to mount root drive RW after reboot.
Reboot