Cyclic equations

Algebra Level 2

For an integer \(n> 2 \), we have real numbers \(a_1, a_2, a_3, a_4, ..., a_n\) such that \[\begin{align} a_2+a_3+a_4+\cdots+a_n&=a_1\\ a_1+a_3+a_4+\cdots+a_n&=a_2\\ &\vdots\\ a_1+a_2+a_3+\cdots+a_{n-1}&=a_n. \end{align}\]

What is the value of \(a_1+a_2+a_3+\cdots+a_n\)?

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