\[\begin{eqnarray} && 10^{10^{10}} \sin\left( \frac{109}{10^{10^{10}}} \right) - 9^{9^{9}} \sin\left( \frac{101}{9^{9^{9}}} \right) \\ &&- 8^{8^{8}} \sin\left( \frac{17}{8^{8^{8}}} \right) + 7^{7^{7}} \sin\left( \frac{76}{7^{7^{7}}} \right) + 6^{6^{6}} \sin\left( \frac{113}{6^{6^{6}}} \right) \end{eqnarray} \]

Evaluate the expression above to 4 significant figures.

**Details and assumptions**

- Angles are measured in degrees.
- No calculators allowed

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