1 The cubic equation \(\mathrm { x } ^ { 3 } + \mathrm { bx } ^ { 2 } + \mathrm { cx } + \mathrm { d } = 0\), where \(b , c\) and \(d\) are constants, has roots \(\alpha , \beta , \gamma\). It is given that \(\alpha \beta \gamma = - 1\).

1. State the value of \(d\).
2. Find a cubic equation, with coefficients in terms of \(b\) and \(c\), whose roots are \(\alpha + 1 , \beta + 1 , \gamma + 1\).
3. Given also that \(\gamma + 1 = - \alpha - 1\), deduce that \(( \mathrm { c } - 2 \mathrm {~b} + 3 ) ( \mathrm { b } - 3 ) = \mathrm { b } - \mathrm { c }\).