a
\( \cot \frac{A}{2}=\frac{\sin \left(\frac{A+\delta_{\min }}{2}\right)}{\sin \frac{A}{2}} \)

\( \Rightarrow \cos \frac{A}{2}=\sin \left(\frac{A+\delta_{\min }}{2}\right) \)

\( \frac{A+\delta_{\min }}{2}=\frac{\pi}{2}-\frac{A}{2} \)

\( \delta_{\min }=\pi-2 A\)