I usually use guessing to solve equations with trig functions. Yesterday, I came across an equation that I couldn't really write it in a helpful form to guess. My question is, how can I solve equation like that without WolframAlpha? I really want to learn a method to solve trig equations without guessing.

Some of my tires to write in a form that allows me to guess an answer.
\begin{align}
2\*(1+\sin(\theta))\sin(\theta) &= 1 \\
\sin(\theta)+\sin^2(\theta) &= \frac{1}{2} \\
2\sin(\theta)+(1-\cos(2\theta)) &= 1 \\
2\sin(\theta)-\cos(2\theta) &= 0 \\
2\sin(\theta)-\cos^2(\theta)+\sin^2(\theta) &= 0 \\
\end{align}

Thank you.