\[ \large \int_0^\pi \dfrac{dx}{(2-\cos x)^2} = \, ? \]

You are given that for constant \(a> 1\), the equation below holds true, \[ \displaystyle \int_0^\pi \dfrac{dx}{a - \cos x} = \dfrac\pi{\sqrt{a^2-1}} \; . \] With this information, find the exact closed form of the integral above.

Give your answer to 3 decimal places.

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