Fundamentally different

Calculus Level 4

\[ \large \begin{cases} { \displaystyle F(x) = \int_0^x \sec^2 t \, dt } \\ { \displaystyle G(x) = \int_0^x F(t) \, dt } \end{cases} \]

We are given the two integrals above. Evaluate \( \displaystyle \int_{-\pi /2}^{\pi /2} G(x) \, dx \). Give your answer to 3 decimal places.

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