Find the value of the given expression:
$$\frac{12+3\frac{2}{3}÷\left[1\frac{3}{4}÷\left\{5\frac{1}{4}\times \left(3\frac{3}{5}÷4\frac{1}{2}\right)\right\}\right]}{1\frac{1}{3}\times 5\frac{1}{5}}$$

First, convert all mixed fractions into improper fractions:
* $3\frac{2}{3}=\frac{11}{3}$
* $1\frac{3}{4}=\frac{7}{4}$
* $5\frac{1}{4}=\frac{21}{4}$
* $3\frac{3}{5}=\frac{18}{5}$
* $4\frac{1}{2}=\frac{9}{2}$
* $1\frac{1}{3}=\frac{4}{3}$
* $5\frac{1}{5}=\frac{26}{5}$

Now substitute these into the expression and solve step-by-step using BODMAS rules:

Step 1: Evaluate the Numerator

1. Inner small parenthesis:

$$\frac{18}{5}÷\frac{9}{2}=\frac{18}{5}\times \frac{2}{9}=\frac{4}{5}$$

2. Curly braces:

$$\frac{21}{4}\times \frac{4}{5}=\frac{21}{5}$$

3. Square brackets:

$$\frac{7}{4}÷\frac{21}{5}=\frac{7}{4}\times \frac{5}{21}=\frac{5}{12}$$

4. Complete the numerator addition:

$$\text{Numerator}=12+\frac{11}{3}÷\frac{5}{12}=12+\frac{11}{3}\times \frac{12}{5}=12+\frac{44}{5}=\frac{60+44}{5}=\frac{104}{5}$$

Step 2: Evaluate the Denominator

$$\text{Denominator}=\frac{4}{3}\times \frac{26}{5}=\frac{104}{15}$$

Step 3: Calculate the Final Fraction Value

$$\text{Value}=\frac{\text{Numerator}}{\text{Denominator}}=\frac{\frac{104}{5}}{\frac{104}{15}}=\frac{104}{5}\times \frac{15}{104}=\frac{15}{5}=3$$