Sine & Cosine

Geometry Level 2

If 3cosθsinθ=13\sqrt{3}\cos \theta-\sin \theta=\frac{1}{3} and 0<θ<π2,0 < \theta < \frac{\pi}{2}, the value of 3sinθ+cosθ\sqrt{3}\sin \theta+\cos \theta can be expressed as a3\frac{\sqrt{a}}{3}. What is the value of a?a?

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