Question 12
Let $x_1,x_2,x_3,x_4,x_5,x_6$ be real numbers such that
$$(\tan x_1)(\tan x_2)(\tan x_3)(\tan x_4)(\tan x_5)(\tan x_6)=1.$$
Let $A$ be the maximum value of
$$(\sin x_1)(\sin x_2)(\sin x_3)(\sin x_4)(\sin x_5)(\sin x_6).$$
Determine the value of $\lfloor A^{-1}\rfloor$.
$$(\tan x_1)(\tan x_2)(\tan x_3)(\tan x_4)(\tan x_5)(\tan x_6)=1.$$
Let $A$ be the maximum value of
$$(\sin x_1)(\sin x_2)(\sin x_3)(\sin x_4)(\sin x_5)(\sin x_6).$$
Determine the value of $\lfloor A^{-1}\rfloor$.