If a+b+c+d=4 then find the value of 1/(1-a)(1-b)( 1-c)+1/(1-b) (1-c) (1-d)+1/(1-c) (1-d) (1-a)+1/(1-d)( 1-b) (1-a) .

1/(1-a)(1-b)( 1-c)+1/(1-b) (1-c) (1-d)+1/(1-c)

(1-d) (1-a)+1/(1-d)( 1-b) (1-a) .

By taking LCM,

=4-[a+b+c+d] / [1-a][1-b][1-c][1-d]

=4-4 / [1-a][1-b][1-c][1-d]

=0