











We immediately find that

are possible choices, which makes

, respectively.
If

, we can eliminate the factor of

to get

Note that if

, we have equality, but this goes against our assumption that

. Note that

for all

, which means

is a monotonically increasing function, and is bounded between -1 and 1. On the other hand,

is a monotonically decreasing function that is unbounded. From this you can gather that the two functions never intersect for

(since

is always negative while

is always positive), which means

is the only solution to the equation above. However, this solution is actually extraneous, since the original equation contains a factor of

. So, in fact, the equation above has no solution for

.
That leaves us with

,

, and

.