Let \( f(x)=x \cos x, x \in\left[\frac{3 \pi}{2}, 2 \pi\right] \) a...

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Let \( f(x)=x \cos x, x \in\left[\frac{3 \pi}{2}, 2 \pi\right] \) and \( g \) is the inverse function of \( f \). If \( \int_{0}^{2 \pi} g(x) d x=a \pi^{2}+ \)
\( \mathrm{P} \)
W \( \mathrm{b} \pi+c \), where \( a, b, c \in R \), then find the value of \( 2(a+b+c) \).
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