Separate variables and attempt integration of at least one side

Obtain term $ln\left( {x + 1} \right)$

Obtain term $k{\text{ }}ln{\text{ }}\sin 2\theta $, where $k =  \pm 1$, $ \pm 2$, or $ \pm \frac{1}{2}$

Obtain correct term $\frac{1}{2}ln{\text{ sin}}2\theta $

Evaluate a constant, or use limits $\theta  = \frac{1}{{12}}\pi $, $x = 0$ in a solution containing terms $a{\text{ }}ln\left( {x + 1} \right)$ and $b{\text{ }}ln{\text{ }}\sin 2\theta $

Obtain solution in any form, e.g. $ln\left( {x + 1} \right) = \frac{1}{2}ln{\text{ }}\sin 2\theta  - \frac{1}{2}ln\,\,\frac{1}{2}$  (f.t. on $k =  \pm 1$, $ \pm 2$, or $ \pm \frac{1}{2}$)

Rearrange and obtain $x = \sqrt {\left( {2\sin 2\theta } \right)}  - 1$, or simple equivalent