It is given that

\(\alpha + \beta + \gamma + \delta = 2,\)

\(\alpha^2 + \beta^2 + \gamma^2 + \delta^2 = 3,\)

\(\alpha^3 + \beta^3 + \gamma^3 + \delta^3 = 4.\)

(a) Find the value of \(\alpha \beta + \alpha \gamma + \alpha \delta + \beta \gamma + \beta \delta + \gamma \delta.\)

(b) Find the value of \(\alpha^2 \beta + \alpha^2 \gamma + \alpha^2 \delta + \beta^2 \alpha + \beta^2 \gamma + \beta^2 \delta + \gamma^2 \alpha + \gamma^2 \beta + \gamma^2 \delta + \delta^2 \alpha + \delta^2 \beta + \delta^2 \gamma.\)

(c) It is given that \(\alpha, \beta, \gamma, \delta\) are the roots of the equation

\(6x^4 - 12x^3 + 3x^2 + 2x + 6 = 0.\)

(i) Find the value of \(\alpha^4 + \beta^4 + \gamma^4 + \delta^4.\)

(ii) Find the value of \(\alpha^5 + \beta^5 + \gamma^5 + \delta^5.\)