Too much brute force can kill you!

Geometry Level 5

\[\large{\xi=\frac{\sin0^\circ+\sin\frac{\phi}{n}+\sin\frac{2\phi}{n}+\cdots+\sin\frac{(n-1)\phi}{n}+\sin\phi}{\cos0^\circ+\cos\frac{\phi}{n}+\cos\frac{2\phi}{n}+\cdots+\cos\frac{(n-1)\phi}{n}+\cos\phi}}\]

The above ratio can be expressed in a simplified form. You may want to find that form first.

If \(n=71\) and \(\phi=71^\circ\), then what is the value of \(\xi\)?

Give your answer to three decimal places.

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