To simplify the expression, follow the order of operations (PEMDAS):

1 1/22 3 2/3 - (2 5/6 + 3 5/6 7/23) * 3/5

Convert mixed numbers to improper fractions:

45/22 11/3 - (17/6 + (23 + 20/6) 3/5)

Multiply fractions and perform the arithmetic:

990/66 - (17/6 + (23 6 + 20) 3/5)
15 - (17/6 + (138 + 20) 3/5)
15 - (17/6 + 158 3/5)
15 - (17/6 + 474/5)
15 - (85/30 + 474/5)
15 - (425/150 + 474/5)
15 - (425/150 + 711/150)

Now, find a common denominator for subtraction:

15 - (425/150 + 711/150)
15 - (1136/150)

Subtract the fractions:

15 - 1136/150
15 - 1136/150 = 15 - 568/75
15 - 7.57 = 7.43

Thus, the simplified value of the expression is 7.43.