First, let's simplify the expression inside the parentheses:

(2/9 + 3a - 4/9 - a^2 + 1/9 - 3a)
= (3a - a^2)

Now, let's multiply this simplified expression by (9 - 6a + a^2):

(3a - a^2)(9 - 6a + a^2)
= 3a(9) - 3a(6a) + 3a(a^2) - a^2(9) + a^2(6a) - a^2(a^2)
= 27a - 18a^2 + 3a^3 - 9a^2 + 6a^3 - a^4
= 27a - 18a^2 + 3a^3 - 9a^2 + 6a^3 - a^4

Therefore, the final result is:

27a - 18a^2 + 3a^3 - 9a^2 + 6a^3 - a^4