Consider the equation $$2\tan(2x) = 3\cot(x)$$ What are the $x$ values (in degrees) that satisfy the equation for $0^\circ \leq x \leq 180^\circ$?
When I try to solve it using the identity of $\tan(2x)$, I get two solutions, which are $33.2^\circ$ and $146.8^\circ$.
However, there appears to be a 3rd solution of $90^\circ$; I get this value after graphing the LHS and RHS on Desmos but should it be a valid solution as $3\cot(90^\circ)$ is undefined?
