已知正项数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\)，\(4S_{n}=a_{n}^{2}+2a_{n}.\)
\((1)\)证明：数列\(\{a_{n}\}\)为等差数列，并求\(\{a_{n}\}\)的通项公式；
\((2)\)设\(b_{n}=\dfrac{1}{(a_{n}+1)(a_{n+1}+1)}\)，求数列\(\{b_{n}\}\)的前\(n\)项和\(T_{n}.\)