On occasion, you can maneuver tetrads into seemingly impossible positions, fitting them into covered gaps and what not by quickly rotating them while they are in a state of flux, as described in sliding.
The champion of the Nook Twist (as it is so dubbed by the Tetris cognoscenti) is by far the 'T' tetrad, which is why it has been proven invaluable (at least in part) to most Tetris players. In this example, the player quickly taps the 'B' button to rotate the tetrad counter-clockwise, fitting it snugly in those hideous gaps. If you have Shockwave Flash installed, you can see, in slow motion, just how the T tetrad works its 'magic'.
Case 2: Making the Impossible Possible
This particular situation does not appear to yield potential, but as the seasoned player can prove, a straight tetrad can too do the 'twist'... the Nook Twist, that is. Here, frantic tapping of the 'A' and 'B' buttons while moving the control pad around plays an important role in a positive outcome.
Of course, after this Nook Twist is done, you have to figure out how to stick two Gamma tetrads in there, which is slightly more problematic, although possible!