Solve θ=a(1-sinθ)

$$\theta = a ( 1 - \sin \theta )$$

Solve for a

$$a=-\frac{\theta }{\sin(\theta )-1}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =2\pi n_{1}+\frac{\pi }{2}$$

Steps for Solving Linear Equation

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

$$a\left(1-\sin(\theta )\right)=\theta$$

Use the distributive property to multiply a by 1-\sin(\theta ).

$$a-a\sin(\theta )=\theta$$

Combine all terms containing a.

$$\left(1-\sin(\theta )\right)a=\theta$$

The equation is in standard form.

$$\left(-\sin(\theta )+1\right)a=\theta$$

Divide both sides by 1-\sin(\theta ).

$$\frac{\left(-\sin(\theta )+1\right)a}{-\sin(\theta )+1}=\frac{\theta }{-\sin(\theta )+1}$$

Dividing by 1-\sin(\theta ) undoes the multiplication by 1-\sin(\theta ).

$$a=\frac{\theta }{-\sin(\theta )+1}$$