Find the biggest value of $|a-b|+|b-c|+|c-a|$ when $a^2+b^2+c^2=1$
Given reals $a_1, a_2, \cdots, a_{n - 1}, a_n$ such that $\sum_{i = 1}^na_1^2 = 1$. Calculate the maximum value of $\sum_{cyc}|a_1 - a_2|$.