We have the following:
[tex]\tan 2B=\cot 2B[/tex]resolving for B:
[tex]\begin{gathered} \tan \: 2B-\cot \: 2B=0 \\ \frac{1}{\cot2B}-\cot 2B=0 \end{gathered}[/tex]For this to be true, both have to be 1 or -1, like this
[tex]\begin{gathered} \frac{1}{1}-1=0 \\ 1-1=0 \\ or \\ \frac{1}{-1}-(-1)=0 \\ -1+1=0 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \cot 2B=1\rightarrow B=\frac{\pi}{8}=22.5 \\ \cot 2B=-1\rightarrow B=\frac{3\pi}{8}=67.5 \end{gathered}[/tex]Therefore, B can be 22.5 ° or 67.5 °
