数列\(\{a_{n}\}\)的各项均为正数，其前\(n\)项和为\(S_{n}\)，\(a_{1}=1\)，且\(S_{n}+S_{n+1}=a_{n+1}^{2}.\)
\((1)\)证明：数列\(\{a_{n}\}\)为等差数列；
\((2)\)若数列\(\{b_{n}\}\)满足\(b_{n}+b_{n+1}=a_{n}\)，求数列\(\{b_{n}\}\)的前\(2n\)项和\(T_{2n}.\)