(2) Let $n \geqslant 2, a_{1}, a_{2}, \cdots, a_{n}$ be positive real numbers, determine the largest real number $C_{n}$ such that the inequality: $\frac{a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2}}{n} \geqslant\left(\frac{a_{1}+a_{2}+\cdots+a_{n}}{n}\right)^{2}+C_{n}\left(a_{1}-a_{n}\right)^{2}$. (2010 Central European Mathematical Olympiad)