Solve A=left(1+sin(θ)right)left(tan(θ)+1/cos(θ)right)left(sin(θ)-1right)^2

$$A = \left( 1+ \sin ( \theta ) \right) \left( \tan ( \theta ) + \frac{ 1 }{ \cos ( \theta ) } \right) { \left( \sin ( \theta ) -1 \right) }^{ 2 }$$

Solve for A

$$A=\left(\cos(\theta )\right)^{3}$$

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

Solve for θ

$$\theta =-\arccos(\sqrt[3]{A})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =\arccos(\sqrt[3]{A})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }A\neq 0\text{ and }A\geq -1\text{ and }A\leq 1$$