VN-TST 1990 Problem 5

Given a tetrahedron such that product of the opposite edges is $1$ . Let the angle between the opposite edges be $\alpha$ , $\beta$ , $\gamma$ , and circumradii of four faces be $R_1$ , $R_2$ , $R_3$ , $R_4$ . Prove that $$\sin^2\alpha + \sin^2\beta + \sin^2\gamma\ge\frac {1}{\sqrt {R_1R_2R_3R_4}}$$