Okay, here we have this:
Considering the provided equation, we are going to find the solution in the interval, so we obtain the following:
![\begin{gathered} \sin \mleft(2\theta\mright)=(√(3))/(2),\: 0\le\: \theta<\: 2\pi \\ 2\theta=(\pi)/(3)+2\pi n,\: 2\theta=(2\pi)/(3)+2\pi n \\ \theta=(\pi)/(6)+\pi n,\: \theta=(\pi)/(3)+\pi n \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/t5vll304aj07qn2410pa2c2oru5obewsnn.png)
Now we analyze which are the solutions that are within the range, then finally we have:
![\theta=(\pi)/(6),\: \theta=(\pi)/(3),\: \theta=(7\pi)/(6),\: \theta=(4\pi)/(3)](https://img.qammunity.org/2023/formulas/mathematics/college/23zlfvdnro502453zxw8scb6o52xut74dd.png)
The above values are the solution set of the equation.