Express \(4 \sin \theta \sin \left( \theta + 60 ^ { \circ } \right)\) in the form
$$a + R \sin ( 2 \theta - \alpha ) ,$$
where \(a\) and \(R\) are positive integers and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\).
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Hence find the smallest positive value of \(\theta\) satisfying the equation
$$\frac { 1 } { 5 } + 4 \sin \theta \sin \left( \theta + 60 ^ { \circ } \right) = 0 .$$
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