Expand the left side with \(\cos(u-v)=\cos u\cos v+\sin u\sin v\):

\[ \cos(\theta-60^\circ) =\cos\theta\cos60^\circ+\sin\theta\sin60^\circ =\tfrac12\cos\theta+\tfrac{\sqrt3}{2}\sin\theta. \]

Set equal to \(3\sin\theta\) and rearrange:

\[ \tfrac12\cos\theta+\tfrac{\sqrt3}{2}\sin\theta=3\sin\theta \;\Rightarrow\; \tfrac12\cos\theta=\Big(3-\tfrac{\sqrt3}{2}\Big)\sin\theta. \] \[ \cos\theta=(6-\sqrt3)\,\sin\theta \;\Rightarrow\; \tan\theta=\frac{\sin\theta}{\cos\theta} =\frac{1}{\,6-\sqrt3\,}. \]

Evaluate the principal angle:

\[ \theta=\arctan\!\Big(\frac{1}{6-\sqrt3}\Big) \approx \arctan(0.2343)=13.2^\circ. \]

Tangent is positive in quadrants I and III, so add \(180^\circ\):

\[ \theta=13.2^\circ,\quad 13.2^\circ+180^\circ=193.2^\circ. \]