\[\begin{array}{l} ABCD{\text{ - квадрат}}{\text{, }}AB = 1 \hfill \\ \angle ABN = \angle MAD = \angle QDC = \angle BCP = \frac{\pi }{8} \hfill \\ AT{\text{ - отрезок касательной}} \hfill \\ AT = ? \hfill \\ \end{array}\]