Evaluate:

$\displaystyle \lim_{n\to \infty}(\sqrt{2}-2^{\frac{1}{3}})(\sqrt{2}-2^{\frac{1}{5}})(\sqrt{2}-2^{\frac{1}{7}})....(\sqrt{2}-2^{\frac{1}{2n+1}})$

using Sandwich(Squeeze-play) theorem