There are two parts to the problem
1) Show that $\frac{\pi}{4} \gt \sqrt{2-\sqrt{2}}$
2) Show that $\sum_{n=2}^{\infty} \frac{1}{n^2} \gt \frac{3}{5}$
Incidentally 2) implies 1) and is a stronger result than 1) which has an easier proof.
[Solution]
1) Show that $\frac{\pi}{4} \gt \sqrt{2-\sqrt{2}}$
2) Show that $\sum_{n=2}^{\infty} \frac{1}{n^2} \gt \frac{3}{5}$
Incidentally 2) implies 1) and is a stronger result than 1) which has an easier proof.
[Solution]
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