Moved - Can anyone solve this equation?

cosA=tanB; cosB=tanC; cosC=tanA in a triangle ABC. Find sinA

Hint: Sin(A) = Tan(A) * Cos(A)

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can anyone solve this equation

cos a =tan b
cos b =tan c
cos c =tan a

by substitution sin a =( cos ^2a *sin c)/ sin b

by trial A=22.5deg B= 42.83 deg. C=114.73 deg.
 
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