If \(\alpha, \beta, \gamma\) are such that\( \alpha + \beta + \gamma = 2\), \(\alpha^2 + \beta^2 + \gamma^2 = 6\), \(\alpha^3 + \beta^3 + \gamma^3 = 8\), then what is the value of \(\alpha^4 + \beta^4 + \gamma^4\)?

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