Polynomial with known root cosine

Geometry Level 5

\[ ax^4 - bx^3 - cx^2 + dx + 1 \]

You are given that the polynomial above has a root of \( \cos\left(\frac{2\pi}{15}\right) \) for positive integers \(a,b,c\) and \(d\). Find the value of \(a+b+c+d\).

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