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

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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