One possible solution:
Define
Note that these functions are inverses when

.
Let
\pi)/8) )
be the solutions to

.
Now if
then we know that any solution

satisfies
 = w_n )
for some

.
Apply

to both sides, so we get
Because we have an explicit formula for

we're now done, but we can use part i) to get a nicer form for the solutions.
From part i), we know that
 = i \cot(\theta/2))
for any
 )
on the unit circle.
(Geometrically, this means that

sends the unit circle to the imaginary axis. In other words, all our solutions will be purely imaginary.)
From here, we just need to evaluate
The co-tangent function has periodicity

, so take

to obtain the full set of solutions.
Pedantic note: We show here that every solution

corresponds to a
 )
for some

.
Technically, we should also explain why every
 )
is a valid solution

.
This is because there are exactly eight possible values each for

and

.
None of these values are

or

, so the function

is a one-to-one mapping between these sets.
---
Fun fact:

and

are examples of Möbius transformations - transformations of the type
Such transformations in the complex plane send a line or circle to another line or circle.