Another Trignometric Series

Calculus Level 3

\[ f(x) = 1 - \dfrac{1}{2} \cos x + \dfrac{1 \times 3}{2 \times 4} \cos 2x - \dfrac{1 \times 3 \times 5}{2 \times 4 \times 6} \cos 3x \cdots. \]

\[ \displaystyle \left \lfloor 10000 \times f\left( \dfrac{\pi}{3} \right) \right \rfloor = \ ? \]

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