Farey fractions in arithmetic progression

Question

Let $\mathcal{F}_{Q;r,q}=\{\gamma=\frac{m}{n} | 0\leq m \leq n \leq Q, \gcd(m,n)=1, n \equiv r \mod q, \gcd(r,q)=1\}$. Usually, with no condition on arithmetic progression, then $\# \mathcal{F}_{Q}$ (cardinality) $=\varphi(1)+\varphi(2)+\varphi(3)+\cdots+\varphi(Q)$ $=\frac{3Q^2}{\pi^2}+O(Q\log Q)$ as $Q\rightarrow \infty$, but now how to get the cardinality for $\mathcal{F}_{Q;r,q}$ as $Q \rightarrow \infty$?