March Break 2024 - Problem 3

Let f(\theta) = (16\cos^2(\theta)-16\cos^4(\theta))(3-12\sin^2(\theta)+12\sin^4(\theta)). If the value of \sum\limits_{n=1}^{6} f(3.75n^\circ) is \dfrac{a}{b}, where a and b are relatively prime positive integers, find 10a+b.