Multiply by the non-zero denominator and rearrange: \(\tan\theta=9\sin\theta\). Since \(90^\circ\) is not defined, multiply by \(\cos\theta\) to obtain \(\sin\theta(1-9\cos\theta)=0\). Thus \(\theta=0\) or \(\cos\theta=1/9\), giving \(\boxed{0^\circ,83.6^\circ}\). At 0 the denominator is 1; at the second root it is \(6\sin\theta+1>0\), so both are valid.