Sum of reciprocal squares

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]