D , E , F are three points on the sides ...

`D , E , F` are three points on the sides `B C ,C A ,A B ,` respectively, such that `/_A D B=/_B E C=/_C F A=thetadot` `A^(prime), B ' C '` are the points of intersections of the lines `A D ,B E ,C F` inside the triangle. Show that are of ` A^(prime)B^(prime)C^(prime)=4cos^2theta,` where `` is the area of ` A B Cdot`

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