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Find the average value of the function ...

Find the average value of the function
`f(x) = (cos^(2)x)/(sin^(2)x + 4 cos^(2)x)` over the interval `[0, (pi)/(2)]`. Check directly that this average, equal to `(1)/(6)`, is the value of the function f(x) for a certain `x= xi` lying within the indicated interval.

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