Trigonometric Functions And Equations

Let for some real numbers \(\alpha\) and \(\beta\), \(a = \alpha - i\beta\). If the system of equations \(4ix + (1 + i)y = 0\) and \(8\left( {\cos {{2\pi } \over 3} + i\sin {{2\pi } \over 3}} \right)x + \overline a y = 0\) has more than one solution, then \({\alpha \over \beta }\) is equal to