We determine the maximum number $N_α(d)$ of equiangular lines with fixed angle $\arccosα$ for $α= 1/(1+2\sqrt2)$ in $d$-dimensional Euclidean space: $2,3,4,6,8,10,14,15,16,17,18,20,22$ for $d \in \{2,\dots,14\}$, and $\max(24, \lfloor 3(d-1)/2 \rfloor)$ for $d \ge 15$. This appears to be the first complete determination of $N_α(d)$ in all dimensions $d$ for a fixed nontrivial $α$, since the work of Lemmens and Seidel for $α= 1/3$ in 1973.