Let $PQRS$ be hyperbolic quadrilateral, i.e. a quadrilateral in $\mathbb{H}$ whose sides are hyperbolic geodesic. Let length$(PQ)=l_1$, and length$(PS)=l_2.$ Also $\angle SPQ=\theta_1$, $\angle PSR=\theta_2$, and $\angle PQR=\theta_3.$ It can be proved that $PQRS$ is uniquely determined by $l_1,l_2,\theta_1,\theta_2,\theta_3.$ Suppose $\theta_i\neq\pi/2$ for $i\in\{1,2,3\}$.
Q) Determine a closed formula for $\angle QRS$, length$(QR)$ and length$(SR)$.
PS: 1) I want a closed formula, not a number of equations from where it can be derived.
2) Angles are not $\pi/2.$ So formulas for Saccheri quadrilateral will not work.
3) Any kind of references (except "The geometry of discrete groups" by Beardon and "Foundations of hyperbolic geometry" by Ratcliffe) will be helpful.