We can first simplify the fractions:

2 2/7 = 16/7
2/3 = 4/3
3 5/7 = 24/7
1/3 = 1/3

Now, we can perform the operations:

16/7 - 4/3 + 24/7 - 1/3
= (16/7 + 24/7) - (4/3 + 1/3)
= 40/7 - 5/3
= (120/21) - (35/21)
= 85/21

Therefore, the final answer is 85/21 or 4 1/21.