Question

$$\tan \theta + 2 \tan \theta + 4 \tan 4 \theta + 8 \cot \theta = \cot \theta$$

Solve for θ

$\theta =\pi +arcSin(\frac{1}{10}\left(55+5\times 51^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{159}\pi \text{, }n_{159}\in \mathrm{Z}$
$\theta =\left(-1\right)arcSin(\frac{1}{10}\left(55+5\times 51^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{172}\pi +2\pi \text{, }n_{172}\in \mathrm{Z}$
$\theta =\pi +\left(-1\right)arcSin(\frac{1}{10}\left(55+5\times 51^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{185}\pi \text{, }n_{185}\in \mathrm{Z}$
$\theta =arcSin(\frac{1}{10}\left(55+5\times 51^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{198}\pi \text{, }n_{198}\in \mathrm{Z}$
$\theta =\pi +arcSin(\frac{1}{10}\left(55+\left(-5\right)\times 51^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{211}\pi \text{, }n_{211}\in \mathrm{Z}$
$\theta =\left(-1\right)arcSin(\frac{1}{10}\left(55+\left(-5\right)\times 51^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{224}\pi +2\pi \text{, }n_{224}\in \mathrm{Z}$
$\theta =\pi +\left(-1\right)arcSin(\frac{1}{10}\left(55+\left(-5\right)\times 51^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{237}\pi \text{, }n_{237}\in \mathrm{Z}$
$\theta =arcSin(\frac{1}{10}\left(55+\left(-5\right)\times 51^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{250}\pi \text{, }n_{250}\in \mathrm{Z}$