Show that any quadrilateral can become cyclic by changing angles.

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Given a convex quadrilateral with given side lengths $a$, $b$, $c$, $d$ in that order (meaning that side a intersects $d$, $b$; side $b$ intersect $a$, $c$ e.t.c.), show that it is possible to "make" this a cyclic quadrilateral just by changing the angles while preserving the side lengths and order in which they appear.