Right now, as noted earlier, you're using only your 3 TB disk--the 3 x 1 TB disks are just burning watts and accomplishing nothing. You have no redundancy--if that one drive dies, you will lose all the data that's on it. Contrary to your statement that you're low on space, you're only using about 1/3 of your capacity right now, though you appear to have set quotas on some of your datasets. But still, more storage is always a good thing, right?
So, the question is, what do you want to accomplish? I've been operating on the assumption that you want your data to survive at least one disk failure, because most of the people here are using FreeNAS because they care about their data. If that's the case, your options are very limited. But I could be wrong--if you're just wanting to maximize storage space, and don't care if a disk failure will result in loss of all your data, you have some other options.
You've said that you want to use your existing 3 TB disk, plus your incoming 2 x 6 TB disks. If you want redundancy (i.e., the ability to survive a disk failure), I can only think of two ways to do that, and both have significant drawbacks. First, you could set them up in a three-way mirror. This would be extraordinarily wasteful of space, resulting in only 3 TB (2.7 TiB) of net capacity from 15 TB of disk space--but it would allow your data to survive the failure of any two disks. The other option would be to create a RAIDZ volume using the three disks. This would not be quite as wasteful of space as the three-way mirror, but you'd still only get 6 TB (5.4 TiB) capacity for your 15 TB of disk space, since RAIDZ is limited by the capacity of the smallest disk in the vdev. You'd also need to back up all your data, destroy your pool, and create a new one for the data.
Assuming you do want some redundancy, I'd suggest a two-way mirror of your 2 x 6 TB disks. It gives you the same capacity as the RAIDZ with only two disks, and will still tolerate the failure of either disk. You can then repurpose your 3 TB disk (and your 3 x 1 TB disks) for whatever other application seems good to you. The method I'd suggest for doing this would be, first, to add one of the 6 TB disks as a mirror of your current 3 TB disk (which will involve some tinkering on the command line), and then, when it's finished syncing the data to that disk, using the web GUI to replace the 3 TB disk with the second 6 TB disk.
As to why you don't want to use the volume manager to extend the volume--if you do, you'll result in a pool that has your existing 3 TB disk striped with either a mirror of the two 6 TB disks, or a stripe of those two disks. In the former case, you'll end up with 9 TB (8.1 TiB) of capacity; in the latter, 15 TB (13.5 TiB). In the latter case, it really doesn't matter--all the disks are striped, and when any of them fails, you'll lose all the data on the pool. But in the former case, you have a false sense of redundancy. You're protected against the loss of one of the 6 TB disks, but if/when the 3 TB disk dies, all your data would be lost.