To start, let's simplify each set of parentheses individually:

(2 - 1/9 + 4/3)
= (2 - 1/9 + 4/3)
= (2 - 1/9 + 12/9)
= (18/9 - 1/9 + 12/9)
= (29/9)

(3/5 + 2/3 - 1/15)
= (9/15 + 10/15 - 1/15)
= (18/15)
= (6/5)

(-2/9 + 1 - 5/3)
= (-2/9 + 9/9 - 15/9)
= (-8/9)

Now, we can combine these simplified results:

(29/9) - (6/5) + (-8/9)

To subtract mixed numbers, we need to find a common denominator. The least common multiple of 9 and 5 is 45.

= (145/45 - 54/45 - 40/45)
= (51/45)
= (17/15)