This discussion is now closed.
\large since \hspace 3 \mathrm{cosec}^2x = \cot^2x + 1
\large thus \hspace 3 (\cot^2x + 1)^2 - \cot^4x = 2 - \cot x
\large let \hspace 3 cot x = y
\large y = \frac{1}{2} \hspace3 y = -1
\large \cot y \hspace3 = \frac{1}{2}, \cot y = -1
y = 63.4,243.4 \hspace4 y = 135, 315
\large the \hspace3 range \hspace3 is \hspace3 90 < 0 < 180