Clone display results in flipped external monitor when in tablet mode

[MatthewSullivanMath]

I have my hdtv hooked up to my tablet pc (gateway m285g). When I rotate the screen 180 degrees so I can go in tablet mode, the hdtv rotates 180 degrees as well and is upside down. Is there a way to prevent the hdtv from rotating as well?
I need clone (duplicate) display and not extended because I'm trying to set this up for my tutoring business so I can write on the laptop and have the students instantly see it on the hdtv. I have a good mount so my current hardware fix is to physically rotate the hdtv upside-down but obviously this takes longer than a couple mouse clicks. Also, my hdtv doesn't have an option to flip the screen but I'd imagine playing around with a remote would take longer than mouse clicks as well. Thanks.

[Zeuxidamas]

I was able to do this routinely using my old HP 2730 EliteBook, which I no longer own. I am pretty sure that I had to go into the Intel GMA dialogue (should be available via an icon in your QuickLaunch tray or via the Control Panel; equivalent settings for rotation should also be available in the Display setting dialogue). I used the Intel GMA app to set these as saved profiles. You should be able to set the HDTV for the orientation that allows you to keep it "right-side up", even when you are in tablet mode.

[MatthewSullivanMath]

I tried playing around with the Intel control panel settings for a while but it seems like it's impossible if you're in clone mode as opposed to extended mode.
Does anyone know of software that can independently rotate a monitor while in clone mode?