The sides \( a, b, c \) (taken in that order) of triangle \( A B C \) are in A.P. If \( \cos \al....

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The sides \( a, b, c \) (taken in that order) of triangle \( A B C \) are in A.P.
If \( \cos \alpha=\frac{a}{b+c}, \cos \beta=\frac{b}{c+a}, \cos \gamma=\frac{c}{a+b} \) then \( \tan ^{2}\left(\frac{\alpha}{2}\right)+\tan ^{2}\left(\frac{\gamma}{2}\right) \quad \) is is equal to
[Note: All symbols used have usual meaning in triangle \( A B C \).]
(1) 1
(2) \( \frac{1}{2} \)
(3) \( \frac{1}{3} \)
(4) \( \frac{2}{3} \)


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