Deviation angle for 1st order diffraction
The grating equation you've used is correct, and in order to find the first order diffraction angle ($n = 1$) you need to use arcsine trigonometric function and carefully place data with respective units:

\begin{align}
n \lambda &amp;= d \sin{\Theta} \tag{1}\\
d &amp;= \frac{\pu{1 mm}}{N}~[\pu{mm}] \tag{2}
\end{align}

where $N$ is number of lines per unit length. Combining (1) and (2) and converting the wavelength from nm to mm:

$$\Theta = \arcsin{\left(\frac{n \lambda}{d}\right)} = \arcsin{\left(\frac{n \lambda N}{\pu{1 mm}}\right)} = \arcsin{\left(\frac{1 \cdot \pu{5e-4 mm} \cdot 560}{\pu{1 mm}}\right)} = 16.26^\circ \tag{3}$$