# Trigonometric Series : Trinity

Calculus Level 5

$\displaystyle 1 + \dfrac{2}{3}\sin^2x + \dfrac{2 \cdot 4}{3 \cdot 5}\sin^4x + \dfrac{2 \cdot 4 \cdot 6}{3 \cdot 5 \cdot 7}\sin^6x + \ldots$

Let $$f(x)$$ denote the value of the above expression.

Then $$\displaystyle f\left( \dfrac{\pi}{24} \right)$$ can be written as

$\dfrac{\pi^a (\sqrt{b} + c)}{d\sqrt{e}}$

where $$b,e$$ are squarefree and $$a,b,c,d,e \in \mathbb N$$. Find the value of $$a+b+c+d+e$$.

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