two years ago,I have conjectures this problem:[stack]

today,I try Find all solutions $a,b,c$

$$(1-a^2)(1-b^2)(1-c^2)=8abc,\quad a,b,c\in \mathbb{Q}^{+}$$  
.
Now I found some solution,such as
$$(a,b,c)=(5/17,1/11,8/9),(1/7,5/16,9/11),(3/4,11/21,1/10),\cdots$$

[stack]:http://math.stackexchange.com/questions/334448/1-a21-b21-c2-8abc-a-b-c-in-mathbbq-has-infinitely-many-sol/336803#336803