If \(A_{1}\), \(A_{2}\), \(A_{3}\) are the arguments of the roots of the complex equation \(Z^3-\alpha^3=0\), where \(\alpha\) is a constant complex number with modulus \(1\), find the value of: \[\sum_{n=1}^{n=3}{\cos(A_{n})+\sin(A_{n})} \].

\(\bullet\) This question is part of the set For the JEE-nius;P

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