Let's break this down step by step:

First, multiply 2/5 by -3:
2/5 * $-3$ = -6/5

Next, subtract 4/5 from -6/5:
-6/5 - 4/5 = -10/5 = -2

Now, divide 4/9 by -2/3:
4/9 ÷ $-2/3$ = 4/9 * $-3/2$ = -12/18 = -2/3

Finally, add 1 to -2/3:
-2/3 + 1 = -2/3 + 3/3 = 1/3

Therefore, the final result is 1/3.