To solve this problem, we need to simplify the expression by following the order of operations (PEMDAS).

First, let's simplify the fractions within the parentheses:
7/15 + 1 13/15 = 1 (15/15) + 1 13/15
= 1 + 1 13/15
= 2 13/15

Now, let's subtract the sum of the fractions from 1 3/4:
1 3/4 - (2 13/15 + 3/8)

Convert the mixed numbers to improper fractions:
1 3/4 = 4/4 + 3/4 = 7/4
2 13/15 = 2 * 15 + 13 / 15 = 43/15

Now, substitute the improper fractions back into the expression:
7/4 - (43/15 + 3/8)

Find a common denominator for the fractions:
7/4 - (43/15 + 9/30)

Perform the addition inside the parentheses:
7/4 - (43/15 + 9/30)
= 7/4 - (86/30 + 9/30)
= 7/4 - 95/30
= 7/4 - 19/6

Convert the fractions to have a common denominator:
7/4 = 105/60
19/6 = 190/60

Subtract the fractions:
105/60 - 190/60 = -85/60 = -17/12

Therefore, 1 3/4 - (2 13/15 + 3/8) = -17/12 or -1 5/12 in mixed number form.