so hmm check the picture below
thus [tex]\bf tan(\theta)=\cfrac{y}{x}\impliedby \textit{using the quotient rule}
\\\\\\
sec^2(\theta)\cfrac{d\theta}{dt}=\cfrac{\frac{dy}{dt}x-y\frac{dx}{dt}}{x^2}\implies \cfrac{1}{cos^2(\theta)}\cdot \cfrac{d\theta}{dt}=\cfrac{\frac{dy}{dt}x-y\frac{dx}{dt}}{x^2}
\\\\\\
\cfrac{d\theta}{dt}=cos^2(\theta)\cdot \cfrac{\frac{dy}{dt}x-y\frac{dx}{dt}}{x^2}\qquad
\begin{cases}
\cfrac{dy}{dt}=3\\
\cfrac{dx}{dt}=2\\
x=5\\
y=7\\
[cos(\theta)]^2=\left( \frac{5}{\sqrt{74}} \right)^2=\frac{25}{74}
\end{cases}
\\\\\\[/tex]
[tex]\bf \cfrac{d\theta}{dt}=\cfrac{\frac{25}{74}(3\cdot 5-7\cdot 2)}{5^2}\implies \cfrac{d\theta}{dt}=\cfrac{\frac{25}{74}(1)}{25}\implies \cfrac{d\theta}{dt}=\cfrac{\frac{25}{74}}{\frac{25}{1}}
\\\\\\
\cfrac{d\theta}{dt}=\cfrac{25}{74}\cdot \cfrac{1}{25}\implies \cfrac{d\theta}{dt}=\cfrac{1}{74}[/tex]
now, are the particles moving away or towards them? well, the dθ/dt is postive, that means, the angle is opening, not closing, so, they're moving away from each other
