Express \(5 \sqrt { 3 } \cos x + 5 \sin x\) in the form \(R \cos ( x - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\).
As \(x\) varies, find the least possible value of
$$4 + 5 \sqrt { 3 } \cos x + 5 \sin x$$
and determine the corresponding value of \(x\) where \(- \pi < x < \pi\).
Find \(\int \frac { 1 } { ( 5 \sqrt { 3 } \cos 3 \theta + 5 \sin 3 \theta ) ^ { 2 } } d \theta\).
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