The expression $-\left(1 \dfrac{2}{3}\right)^2 - 2$ simplifies to approximately $-4.78$.

Would you like further details on how this was calculated, or do you have any other questions?

Here are five related questions to explore:

1. How do you convert a mixed fraction into an improper fraction?
2. What is the process for squaring a fraction?
3. How do negative signs affect operations like squaring?
4. How does the order of operations apply in complex expressions like this?
5. How can you express the result as a fraction?

Tip: When working with mixed fractions, always convert them to improper fractions before applying other operations like squaring.