Not sure what TTT is, but unless it's an advanced yoga program, this shouldn't conflict.
The main muscles that need to be stretched are the triceps, traps, rhomboids, lats, and forearm flexors.
Triceps - the hand behind your back, pull on the elbow with the opposite hand thing. Pretty standard. Depending on how tight it is, hold for 30 - 180 seconds.
Traps - this is a little tricky, so apply any pressure VERY lightly until you get the hang of it. Turn your head to one side, we'll say the left, then bring your chin down to meet your shoulder/upper chest. Now gently apply a little bit of pressure with your left hand by pulling down with your left hand behind your head. Don't do this one if you have any existing neck problems, though. Since you're applying such gentle pressure (as it's the neck), hold for 15 - 120 sec, depending on tightness.
Rhombiods - stick both hands out in front of you and grab on to a pole, then lean back/sit down. These usually aren't very tight on people, so play the time held by ear. I wouldn't go over a minute by any means.
Lats - my favorite is to stand in a doorway, grab onto the left side of the doorframe with my right hand, and lean away from the frame. Using that pole or whatever in the rhomboid stretch would work well, too. You'll have to play with the angle your body is to the support a little to find the right position, but once you do, it's gold. Lats are typically very tight on people, so I'd hold this one around a minute or two.
Gently bend your wrist back to stretch the forearm flexors, no need to get fancy there. Time as needed.
Once you have all the individual muscles stretched out, get into a front squat position (clean grip - crossing your arms as others suggested isn't as stable) without the bar and see how high you can get your elbows - they should stick straight out in front of you, not towards the floor. If it looks like the bar would be on your throat in this position, try to feel what muscle(s) are still tight and stretch them a bit more.
Like I said, it may take a little while to build up the flexibility - don't get frustrated if it takes a week or so. High-bar olympic squats make a good substitution in the meantime.