To solve this expression, we need to multiply the fractions and then add or subtract as necessary.

2/7 2/3 = 4/21
2/3 3/7 = 2/7
5/7 * 1/3 = 5/21

Now we can substitute these values back into the original expression:

4/21 + 2/7 - 5/21

To add fractions, they need to have a common denominator. In this case, the common denominator is 21. So we can rewrite the fractions with the common denominator:

4/21 + 6/21 - 5/21

Now we can add the fractions:

(4 + 6 - 5)/21
= 5/21

Therefore, 2/7 2/3 + 2/3 3/7 - 5/7 * 1/3 simplifies to 5/21.