In a triangle ABC, let A:B:C=1:2:4 then what is the value of {Tan(A) Tan(B) + Tan(B) Tan(C) + Tan(C) Tan(A)}? If [math]\tan^{2}a\tan^{2}b+\tan^{2}b\tan^{2}c+\tan^{2}a\tan^{2}c+2\tan^{2}a\times\tan^{2}b\times\tan^{2}c=1[/math] prove that [math]\sin^2a +\sin^2b+\sin^2c=1[/math]?