7. Given the hyperbola $C: x^{2}-\frac{y}{3}=1$, with left and right foci $F_{1}$ and $F_{2}$, respectively. A line is drawn through point $F_{2}$ intersecting the right branch of the hyperbola $C$ at points $P$ and $Q$, such that $\angle F_{1} P Q=90^{\circ}$. Then the inradius of $\triangle F_{1} P Q$ is $\qquad$
$$
\text { 7. } \sqrt{7}-1 \text {. }
$$

As shown in Figure 4.