Indirect limits

Calculus Level 3

$\large f(x) = \frac{(e^x-1)^4}{\sin \left(\frac{x^2}{\lambda^2} \right) \ln \left(1 + \frac{x^2}2 \right) }$

For non-zero $x$ , denote the function $f$ as above. If $f(0)= 8$ and $f$ is continuous then what is the possible value of $\lambda$ ?