Suppose we are given four angles $\alpha$, $\beta$, $\gamma$ and $\delta$. For a quadrilateral to exist with interior angles $\alpha$, $\beta$, $\gamma$ and $\delta$ in the hyperbolic plane we must have $\alpha +\beta+\gamma+\delta< 2\pi$. But what are the sufficient conditions for the existence of a hyperbolic quadrilateral with interior angles $\alpha$, $\beta$, $\gamma$ and $\delta$ satisfying $\alpha +\beta+\gamma+\delta< 2\pi$?

I have tried using some hyperbolic trigonometric formulas to obtain some conditions but couldn't reach anywhere. Any kind of help will be appreciated.


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