First, simplify the division inside the parentheses:

(-5 6/7 ÷ 1 1/41) × (-4 1/3)

Convert the mixed numbers to improper fractions:

((-41/7) ÷ (41/41)) × (-13/3)

Now divide the fractions:

((-41/7) ÷ (41/41)) = (-41/7) × (41/41) = -41

Now multiply by -13/3:

-41 × -13/3 = 533/3

Therefore, the final result is 533/3 or 177 2/3.