I have no idea at all what to do on this
I got $\cos^{-1} \left(\frac{r\sin \theta+1}{3} \right) = \theta$
Which can be
$\cos^{-1} \left(\frac{r\sin \left(\cos^{-1} \left(\frac{r\sin \theta+1}{3} \right) \right)+1}{3} \right) = \theta$
$\cos^{-1} \left(\frac{r\sin \left(\cos^{-1} \left(\frac{r\sin \left(\cos^{-1} \left(\frac{r\sin \theta+1}{3} \right) \right)+1}{3} \right) \right)+1}{3} \right) = \theta$
So that obviously seems wrong, other than that 30 minutes of work has produced nothing.