The points $(0,0,0),$ $(a,1,1),$ $(1,b,1),$ and $(1,1,c)$ are coplanar, where $a \neq 1,$ $b \neq 1,$ and $c \neq 1.$  Compute
\[\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The points $(0,0,0),$ $(a,1,1),$ $(1,b,1),$ and $(1,1,c)$ are coplanar, where $a \neq 1,$ $b \neq 1,$ and $c \neq 1.$  Compute
\[\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
The points $(0,0,0),$ $(a,1,1),$ $(1,b,1),$ and $(1,1,c)$ are coplanar, where $a \neq 1,$ $b \neq 1,$ and $c \neq 1.$  Compute
\[\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}.\]
train