Solve {l}{(1.8cosθ+0.2)t=1230}{1.8tsinθ=2680}

$$\left. \begin{array} { l } { ( 1.8 \cos \theta + 0.2 ) t = 1230 } \\ { 1.8 t \sin \theta = 2680 } \end{array} \right.$$

Solve for θ, t (complex solution)

$$\theta =2\pi n_{1}-i\ln(\frac{\left(123+268i\right)\sqrt{6971369}+\left(-71824+32964i\right)}{782577})\text{, }n_{1}\in \mathrm{Z}\text{, }t=-\frac{4347650\left(\left(-123-268i\right)\sqrt{6971369}+\left(71824-32964i\right)\right)}{\left(-56695+65928i\right)\sqrt{6971369}+\left(848644035+1872381464i\right)}\approx 1573.334385389-5.605555819 \cdot 10^{-14}i$$

$$\theta =2\pi n_{2}-i\ln(\frac{\left(-123-268i\right)\sqrt{6971369}+\left(-71824+32964i\right)}{782577})\text{, }n_{2}\in \mathrm{Z}\text{, }t=-\frac{4347650\left(\left(123+268i\right)\sqrt{6971369}+\left(71824-32964i\right)\right)}{\left(56695-65928i\right)\sqrt{6971369}+\left(848644035+1872381464i\right)}\approx -1727.084385389+1.350932731 \cdot 10^{-13}i$$

Solve for θ, t

$$\theta =2\pi n_{3}-\arcsin(\frac{268\left(123-\sqrt{6971369}\right)}{782577})+\pi \text{, }n_{3}\in \mathrm{Z}\text{, }t=\frac{-5\sqrt{6971369}-615}{8}\text{, }n_{3}\in \mathrm{Z}\text{, }\nexists n_{2}\in \mathrm{Z}\text{ : }2\pi n_{3}-\arcsin(\frac{268\left(123-\sqrt{6971369}\right)}{782577})+\pi =2\pi n_{2}+\pi +\arccos(\frac{1}{9})\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }2\pi n_{3}-\arcsin(\frac{268\left(123-\sqrt{6971369}\right)}{782577})+\pi =2\pi n_{1}+\pi -\arccos(\frac{1}{9})$$

$$\theta =2\pi n_{4}+\arcsin(\frac{268\left(\sqrt{6971369}+123\right)}{782577})\text{, }n_{4}\in \mathrm{Z}\text{, }t=\frac{5\sqrt{6971369}-615}{8}\text{, }n_{4}\in \mathrm{Z}\text{, }\nexists n_{2}\in \mathrm{Z}\text{ : }2\pi n_{4}+\arcsin(\frac{268\left(\sqrt{6971369}+123\right)}{782577})=2\pi n_{2}+\pi +\arccos(\frac{1}{9})\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }2\pi n_{4}+\arcsin(\frac{268\left(\sqrt{6971369}+123\right)}{782577})=2\pi n_{1}+\pi -\arccos(\frac{1}{9})$$