I would tackle it this way:
First install Windows 7 (At this point I don't believe you have to worry about partitioning) on your clean HDD.
Then install Ubuntu, during which I would then make the 3 partitions using Ubuntu's tool for this on its liveCD. (Resizing the Windows7 to desired size, and putting Ubuntu on the 2nd partition).
Last, install Backtrack onto the third partition.
I believe Backtrack will use Grub2 by default, and after installing Backtrack, at boot you should see all three OS(s) on the boot menu ^^ (You might actually see more, including the safemode options I think)
The reason I would Install Windows first, is because if you try to install it after Linux, it will mess up the Bootloader I think.
I hope this is good advice