A priori, segundo enunciado, sabemos que: \begin{matrix} f( \ f(\pi/2) \ ) &=& 0 \end{matrix}Analisando agora $f(\pi/2)$ pela lei da função, \begin{matrix} f(\pi/2) &=& {{\dfrac{\pi}{2}}} - {{\dfrac{2a}{\pi}}} &<& {{\dfrac{\pi}{2}}} \end{matrix}Assim, \begin{matrix} f \left({{\dfrac{\pi}{2}}} - {{\dfrac{2a}{\pi}}}\right) &=& a \left({{\dfrac{\pi}{2}}} - {{\dfrac{2a}{\pi}}} + {{\dfrac{\pi}{2}}} \right) &=& 0 &\therefore& \fbox{$a = {\dfrac{\pi^2}{2}}$} \end{matrix}\begin{matrix} Letra \ (D) \end{matrix}