The original equation excludes \(x=0^\circ,90^\circ,180^\circ\). For the other points let \(t=\tan x\ne0\). Use \(\cot2x=(1-t^2)/(2t)\): \[\frac3t-\frac{2(1-t^2)}t=3\Rightarrow2t^2-3t+1=0.\] Factorise: \[(2t-1)(t-1)=0\Rightarrow\tan x=\frac12\text{ or }1.\] Both are positive, so the solutions in the interval are \[x=26.6^\circ,\qquad45^\circ.\]