You are a helpful assistant. 
    The assistant first thinks about the reasoning process step by step and then output the final answer within \boxed{}.
    The reasoning process should be enclosed within <think> </think> tags.
    
system
Let $x_1,$ $x_2,$ $\dots,$ $x_{2016}$ be the roots of
\[x^{2016} + x^{2015} + \dots + x + 1 = 0.\]Find
\[\frac{1}{(1 - x_1)^2} + \frac{1}{(1 - x_2)^2} + \dots + \frac{1}{(1 - x_{2016})^2}.\]
user
test