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

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

This question is from the set polynomial with known trigo root.

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