Solution
= Solution
Near $k=0$, $E=E_0-6\mu+\mu\sum_i(k\cdot a_i)^2+O(k^4)$. The quadratic form has <eigenvalues> $a^2/4,a^2/4,a^2$ along its principal axes, so comparison with $\hbar^2k_j^2/(2m_j^*)$ gives $m^*=2\hbar^2/(\mu a^2)$ twice and $m^*=\hbar^2/(2\mu a^2)$ once (with signs interpreted at the selected band extremum).