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Just to expand on this.
What diffs ratios are available for the Sprint.
Guessing 3:45.1 may be a bit tall for the 13B Sprint.
RX8 is 4:4.1 standard.
There is more to it than just gearing! You have to figure in wheel size as well, the RX8 probably runs on 17 or 18" wheels not the 13" Triumph rims. And whilst the 13b revs MUCH higher than any Triumph motor can, how much torque goes with it?
There IS only one diff for Sprint, that is the 3.45 and it's the only Dolomite axle that can handle more than 120 or so horses. (250+ for a Sprint axle in good order)
Which is a bit limiting, HOWEVER the Sprint diff is related quite closely to that in the Stag, TR4-6 and the big saloons (2000/2500/2.5Pi) Sufficiently so, that a CW/P assembly from one of those could be persuaded into a Sprint case by someone who knows what they are doing. Besides the stock Sprint 3.45, the other choices offer 3.7 and 4.11 and at least one other I can't remember. (note, The TR8s 3.08 WON'T fit, but you don't want to go in that direction anyway!)
My advice is to bung in the 3.45 and see how it goes! If it turns out too tall, have a word with Mike Papworth about getting a custom axle built with a different ratio. Better still, look at a Gripper or similar LSD!
Steve