To solve this equation, we must distribute and simplify on both sides:

Left side:
2*(2/5z + 1) + 3 1/3
= 4/5z + 2 + 3 1/3
= 4/5z + 2 + 10/3
= 4/5z + 6/3 + 10/3
= 4/5z + 16/3

Right side:
4 - 1/2*(4/5z - 1)
= 4 - 2/5z + 1
= 5 - 2/5z

Equating the two sides:
4/5z + 16/3 = 5 - 2/5z

Now, we need to solve for z:

4/5z + 2/3 - 5 + 2/5z = 0
6/5z - 13/3 = 0
6z - 13*5/3 = 0
6z - 65/3 = 0
6z = 65/3
z = 65/18

Therefore, the solution to the equation 2(2/5z + 1) + 3 1/3 = 4 - 1/2(4/5z - 1) is z = 65/18.