To calculate this expression, we need to first simplify the absolute values and then perform the operations:

Absolute value of (5 2/3 - 7):
5 2/3 = 17/3
|17/3 - 7| = |17/3 - 21/3| = | -4/3| = 4/3

Absolute value of 2:
|2| = 2

Absolute value of -1/9:
|-1/9| = 1/9

Now, we can substitute these values back into the expression:

4/3 - 2 - 1/9

Now, let's find a common denominator to add the fractions:

36/27 - 54/27 - 3/27 = (36 - 54 - 3) / 27 = -21/27 = -7/9

Therefore, the final result is -7/9.