Estimating $\pi$

Let $n$ be an even integer with $n \geqslant 6$, and let $S_n$ denote the area of a regular $n$-gon inscribed in the unit circle.

1. Prove that

2. Given $1.732 < \sqrt{3} < 1.733$ and $3.105 < S_{24} < 3.106$, prove that $3.14 < \pi < 3.15$.