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 $$(a,b,c)=(5/17,1/11,8/9),(1/7,5/16,9/11),(3/4,11/21,1/10),\cdots$$

$$(a,b,c)=(\dfrac{4p}{p^2+1},\dfrac{p^2-3}{3p^2-1},\dfrac{(p+1)(p^2-4p+1)}{(p-1)(p^2+4p+1)}),p>2+\sqrt{3},p\in\mathbb {Q}^{+}$$

My Question: Have other form solution(or find all solutions?)? [stack]:http://math.stackexchange.com/questions/334448/1-a21-b21-c2-8abc-a-b-c-in-mathbbq-has-infinitely-many-sol/336803#336803