Question 5 - A-Level Maths

Show that the equation $$10 \operatorname { cosec } ^ { 2 } x = 16 - 11 \cot x$$ can be written in the form $$10 \cot ^ { 2 } x + 11 \cot x - 6 = 0$$
Hence, given that $10 \operatorname { cosec } ^ { 2 } x = 16 - 11 \cot x$, find the possible values of $\tan x$.