$(\tan ^{-1}x)^2+(\cot ^{-1}x)^2=\large\frac{5 \pi^2}{8}$$=>x=$

Question

\[\begin {array} {1 1} (a)\;-1 & \quad (b)\;1 \\ (c)\;0 & \quad (d)\;\pi \sqrt {\frac{5}{8}} \end {array}\]