Quintuple of cosine

Geometry Level 3

cos5θ=acos5θ+bcos3θ+ccosθ\large \cos{5\theta}=a\cos^5{\theta}+b\cos^3{\theta}+c\cos{\theta}

Given that the above is a trigonometric identity for constants a,ba,b and cc, find the value of a2+b2+c2a^2+b^2+c^2.

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