1/(1-2a)+1/(1-2b)+1/(1-2c)
=(1-2a-2b+4ab+1-2a-2c+4ac+1-2b-2c+4bc)/(1-2a)(1-2b)(1-2c)
=(3-4(a+b+c)+4ab+4ac+4bc)/(1-2a)(1-2b)(1-2c)
=(-1+4ab+4ac+4bc)/((1-2a-2b+4ab)(1-2c))
=(-1+4ab+4ac+4bc)/(1-2c-2a+4ac-2b+4bc+4ab-8abc)
=1
-1+4ab+4ac+4bc=1-2(a+b+c)+4ac+4bc+4ab-8abc
-1=1-2-8abc
abc=0