$\text{Method I}:$
The angle between hour hand and minute hand of a clock at $H$ hours and $M$ minutes is given by $$\theta = 30H – \dfrac{11M}{2}$$So, at $03:15$ we get their difference as $30\times 3 - \frac{11(15)}{2}$
$\qquad= 90 – 82.5 = 7.5^{\circ}$

$\text{Method II}:$

$1 H = \frac{360}{12} = 30^{\circ}$

$15 M = \frac{1}{4}H = \frac{30^{\circ}}{4} = 7.5^{\circ}$