Which Formula Should I Apply? (Part 2)

Geometry Level 3

Evaluate

\[\frac{241}{2-\cot^{2} (9^{\circ})}+\frac{241}{2-\cot^{2} (27^{\circ})}+\frac{241}{2-\cot^{2} (45^{\circ})}\\ +\frac{241}{2-\cot^{2} (63^{\circ})}+\frac{241}{2-\cot^{2} (81^{\circ})} . \]

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