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

10 - 2 \cdot \frac{2}{11} \cdot (7 \frac{1}{3} + 1.6) : 1 \frac{1}{9}

First, we convert the mixed numbers to improper fractions:

10 - 2 \cdot \frac{2}{11} \cdot \left(7 + \frac{1}{3} + 1 + \frac{3}{5}\right) : \frac{10}{9}

10 - 2 \cdot \frac{2}{11} \cdot \left(7 + \frac{10}{3}\right) : \frac{10}{9}

10 - 2 \cdot \frac{2}{11} \cdot \frac{31}{3} : \frac{10}{9}

10 - \frac{4}{11} \cdot \frac{31}{3} : \frac{10}{9}

10 - \frac{124}{33} : \frac{10}{9}

Now, to divide by a fraction, we can multiply by its reciprocal:

10 - \frac{124}{33} \cdot \frac{9}{10}

10 - \frac{1116}{330}

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

10 - \frac{186}{55}

Now, subtract:

\frac{550}{55} - \frac{186}{55} = \frac{364}{55}

Therefore, the simplified expression is:

\frac{364}{55}