Solve {l}{tan(θ)=-3/4}{a=sin(θ/2)}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { \tan(\theta) = -\frac{3}{4} }\\ { a = \sin(\theta / 2) }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for θ, a, b (complex solution)

$$\theta =\pi n_{1}+\pi -\arctan(\frac{3}{4})$$

$$n_{1}\in \mathrm{Z}$$

$$a=\sin(\frac{\arctan(\frac{3}{4})}{2})\sin(\frac{\pi n_{1}}{2})+\cos(\frac{\arctan(\frac{3}{4})}{2})\cos(\frac{\pi n_{1}}{2})$$

$$n_{1}\in \mathrm{Z}$$

$$b\in \cup n_{1},\sin(\frac{\arctan(\frac{3}{4})}{2})\sin(\frac{\pi n_{1}}{2})+\cos(\frac{\arctan(\frac{3}{4})}{2})\cos(\frac{\pi n_{1}}{2})$$

$$n_{1}\in \mathrm{Z}$$

Solve for θ, a, b

$$\theta =2\pi n_{1}+2\pi -\arcsin(\frac{3}{5})\text{, }n_{1}\in \mathrm{Z}\text{, }a=\sin(\frac{\arcsin(\frac{3}{5})}{2})\left(-1\right)^{n_{1}}\text{, }n_{1}\in \mathrm{Z}\text{, }b=\sin(\frac{\arcsin(\frac{3}{5})}{2})\left(-1\right)^{n_{1}}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =2\pi n_{2}+\pi -\arcsin(\frac{3}{5})\text{, }n_{2}\in \mathrm{Z}\text{, }a=\cos(\frac{\arcsin(\frac{3}{5})}{2})\left(-1\right)^{n_{2}}\text{, }n_{2}\in \mathrm{Z}\text{, }b=\cos(\frac{\arcsin(\frac{3}{5})}{2})\left(-1\right)^{n_{2}}\text{, }n_{2}\in \mathrm{Z}$$