Solve s^2=c_{1}(θ+sinθ)

$$s ^ { 2 } = c _ { 1 } ( \theta + s i n \theta )$$

Solve for c_1

$$\left\{\begin{matrix}c_{1}=\frac{s^{2}}{\sin(\theta )+\theta }\text{, }&\sin(\theta )+\theta \neq 0\\c_{1}\in \mathrm{R}\text{, }&s=0\text{ and }\sin(\theta )+\theta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply c_{1} by \theta +\sin(\theta ).

$$s^{2}=c_{1}\theta +c_{1}\sin(\theta )$$

Swap sides so that all variable terms are on the left hand side.

$$c_{1}\theta +c_{1}\sin(\theta )=s^{2}$$

Combine all terms containing c_{1}.

$$\left(\theta +\sin(\theta )\right)c_{1}=s^{2}$$

The equation is in standard form.

$$\left(\sin(\theta )+\theta \right)c_{1}=s^{2}$$

Divide both sides by \theta +\sin(\theta ).

$$\frac{\left(\sin(\theta )+\theta \right)c_{1}}{\sin(\theta )+\theta }=\frac{s^{2}}{\sin(\theta )+\theta }$$

Dividing by \theta +\sin(\theta ) undoes the multiplication by \theta +\sin(\theta ).

$$c_{1}=\frac{s^{2}}{\sin(\theta )+\theta }$$

Solve for s

$$s=\sqrt{c_{1}\left(\sin(\theta )+\theta \right)}$$

$$s=-\sqrt{c_{1}\left(\sin(\theta )+\theta \right)}\text{, }\left(c_{1}\leq 0\text{ or }\sin(\theta )+\theta \geq 0\right)\text{ and }\left(c_{1}\geq 0\text{ or }\sin(\theta )+\theta \leq 0\right)$$