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Two trains intersect at an angle theta

Source:

May 10, 2012
trigonometry

Problem Statement

Two train lines intersect each other at a junction at an acute angle θ\theta. A train is passing along one of the two lines. When the front of the train is at the junction, the train subtends an angle α\alpha at a station on the other line. It subtends an angle β(<α)\beta (<\alpha) at the same station, when its rear is at the junction. Show that tan⁡θ=2sin⁡αsin⁡βsin⁡(α−β)\tan\theta=\frac{2\sin\alpha\sin\beta}{\sin(\alpha-\beta)}
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