In Levine on page 90 it is stated that the following sequence is exact
$$ 0 \to bP^{n+1} \to \Theta^n \to Coker(J_n) $$
where $\Theta^n$ is the group of exotic spheres, $bP^{n+1}$ is the subgroup of those exotic spheres that have as their boundary a parallelizable manifold and $J_n$ is the $J$-homomorphism. My question will be how to recover the $\Theta^n$.
What I know:
By corollary 2.2 $bP^n = 0$ for $n$ odd so that if $n$ is even $\Theta^n \cong Coker(J_n)$ where $Coker(J_n)$ are known for all $n$.
For some $n$ (namely $n\neq 2^k -1, n \neq 2^k -2$) Brumfield and Frank proved that the following sequence splits $$ 0\to bP^{n+1}\to \Theta^n \to T\Theta^n \to 0$$ so that the case of odd $n$ of the form $n\neq 2^k -1$ is also known: $\Theta^n \cong bP^{n+1} \oplus T\Theta^n$ where $bP^{n+1} $ and $T\Theta^n$ are known. (or so I believe, correct me if I'm wrong. Is there anywhere other than the original work where this is discussed? I don't have access to the paper)
So I have two questions: where can I read about the Brumfiel/Frank work that shows the sequence splits and where can I read about the sequence and $\Theta^n$ for $n=2^k - 1$?