Quick! Where's the Chebyshev Table?

Geometry Level 5

\[ \large{\begin{eqnarray} \cos(2x) &=& 2\cos^2(x) - 1 \\ \cos(3x) &=& 4\cos^3(x) - 3\cos(x) \\ \cos(4x) &=& 8\cos^4(x) - 8\cos^2(x)+1 \\ \end{eqnarray} }\]

Above shows the first 3 examples of writing \(\cos(nx) \) in terms of a polynomial of \(\cos(x) \) for positive integer \(n\).

If we write \(\cos(2015x) \) in terms of a polynomial of \(\cos(x) \), what is the coefficient of \(\cos^3(x) \)?

If the value is \(Y\), submit your answer as \(Y \div 2015 \).

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