Sine & Cosine

Geometry Level 2

If \(\sqrt{3}\cos \theta-\sin \theta=\frac{1}{3}\) and \(0 < \theta < \frac{\pi}{2},\) the value of \(\sqrt{3}\sin \theta+\cos \theta\) can be expressed as \(\frac{\sqrt{a}}{3}\). What is the value of \(a?\)

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