Answer
Please see the work below.
Work Step by Step
Total path difference
$=dsin\theta(\frac{\phi}{2})+dsin(\frac{\phi}{2})=2dsin(\frac{\phi}{2})$
The constructive interference and principal maximum occur when the path difference is an integral multiple of the wavelength $\lambda$. Thus, $2dsin(\frac{\phi}{2})=m\lambda$, where $m=0,\pm1,\pm 2........$