Answer
$\approx12^\circ$
Work Step by Step
We know, for bright fringes in a diffraction grating, that
$$m\lambda=d\sin\theta$$
and for the first order, $m=1$
$$ \lambda=d\sin\theta$$
So, the angle of the first order is given by
$$\theta=\sin^{-1}\left[\dfrac{\lambda}{d}\right] $$
Noting that $d=\dfrac{1}{N}\times10^{-2}\;\rm m$
$$\theta=\sin^{-1}\left[\dfrac{N\lambda}{10^{-2}}\right] $$
Therefore, the angular separation is given by
$$\Delta \theta=\theta_2-\theta_1$$
$$\Delta \theta=\bigg|\sin^{-1}\left[\dfrac{N\lambda_2}{10^{-2}}\right] -\sin^{-1}\left[\dfrac{N\lambda_1}{10^{-2}}\right] \bigg|$$
Plugging the given;
$$\Delta \theta=\bigg|\sin^{-1}\left[\dfrac{7700\times 410\times10^{-9}}{10^{-2}}\right] -\sin^{-1}\left[\dfrac{7700\times 656\times10^{-9}}{10^{-2}}\right] \bigg|= $$
$$\Delta \theta=\color{red}{\bf11.94^\circ}$$