If the vectors \(a\hat i + \hat j + \hat k,\;\hat i + b\hat j + \hat k\) and \(\hat i + \hat j + c\hat k\;\left( {a,\;b,\;c \ne 1} \right)\) are coplanar, then the value of \(\frac{1}{{1 - a}} + \frac{1}{{1 - b}} + \frac{1}{{1 - c}}\) is equal to
1
1
2
2
3
a + b + c
4
abc