2018 Fermat Problem 17

In the diagram, square PQRS has side length 2. Points M and N are the midpoints of SR and RQ, respectively. The value of \cos(\angle MPN) is

\textbf{(A)}\ \frac{4}{5}\quad \textbf{(B)}\ \frac{\sqrt{2}}{2}\quad \textbf{(C)}\ \frac{\sqrt{5}}{3}\quad \textbf{(D)}\ \frac{1}{3}\quad \textbf{(E)}\ \frac{\sqrt{3}}{2}

If there are no answer choices shown, enter a numerical answer.

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