第 025 题 / 112

设函数 $f\left( x\right) = {2x} - \cos x$ ， $\left\{ {a}_{n}\right\}$ 是公差为 $\frac{\pi }{8}$ 的等差数列， $f\left( {a}_{1}\right) + f\left( {a}_{2}\right) + \cdots + f\left( {a}_{5}\right) = {5\pi }$ ，则 ${\left\lbrack f\left( {a}_{3}\right) \right\rbrack }^{2} - {a}_{1}{a}_{5} =$
A. 0
B. $\frac{1}{16}{\pi }^{2}$

C. $\frac{1}{8}{\pi }^{2}$

D. $\frac{13}{16}{\pi }^{2}$