$If \sin \left(\frac{\pi cot \theta }{4}\right) = \cos \left(\frac{\pi \tan \theta }{4}\right)$ and $\theta$ is in the first quadrant, then $\theta$=

$$\begin{gathered} \sin \left(\frac{\mathrm{\pi } \cot \mathrm{\theta }}{4}\right) =\cos \left(\frac{\mathrm{\pi } \tan \mathrm{\theta }}{4}\right) \\ \sin \left(\frac{\mathrm{\pi } \cot \mathrm{\theta }}{4}\right) \\ =\sin \left(\frac{\mathrm{\pi }}{2}-\frac{\mathrm{\pi } \mathrm{tan\theta }}{4}\right) \\ \frac{\mathrm{\pi cot\theta }}{4}=\frac{\mathrm{\pi }}{2}-\frac{\mathrm{\pi tan\theta }}{4} \\ \mathrm{cot\theta }+\mathrm{tan\theta }=2 \\ \frac{2\mathrm{tan\theta }}{1+{\tan }^2\mathrm{\theta }}=1 \\ \sin 2\mathrm{\theta }=\sin \frac{\mathrm{\pi }}{2} \\ 2\mathrm{\theta }=\frac{\mathrm{\pi }}{2} \Rightarrow \mathrm{\theta }=\frac{\mathrm{\pi }}{4} \end{gathered}$$