We can rewrite [tex]cot(45^{\circ}+2\theta)[/tex] as [tex]tan(90^{\circ}-(45^{\circ}+2\theta)[/tex] [tex]\Rightarrow[/tex] [tex]cot(45^{\circ}+2\theta)[/tex] equals to [tex]tan(45^{\circ}-2\theta)[/tex].
Now we need to take an [tex]arctan[/tex] of both sides.
[tex]\theta = 45^{\circ}-2\theta+180n^{\circ}
\\3\theta = 180n^{\circ}+45^{\circ}
\\\theta = 60n^{\circ}+15^{\circ}
\\\theta = 15^{\circ}[/tex]
Your answer is [tex]15^{\circ}[/tex].
