First, let's simplify the expression inside the parentheses:
(-4 1/18 - 1 1/5 + 3 8/15)
= (-73/18 - 6/5 + 73/15)
= (-365/90 - 108/90 + 486/90)
= (13/90)

Now, let's multiply by 3:
(13/90) * 3 = 39/90

Next, subtract 2.6:
(39/90) - 2.6
= (13/30) - (26/10)
= (13/30) - (78/30)
= -65/30
= -13/6

Therefore, the final answer is -13/6.