Sides a , b , c of `!ABC` are in A.P. and `costheta_(1)=a/(b+c)costheta_(2)=b/(a+c),costheta_(3)=c/(a+b)` , then `tan^(2)(theta_(1))/2+tan^(2)(theta_(3))/2`=

Options

A. `2//3`
B. 1
C. `sqrt5//3`
D. none of these

Explanation

To solve the problem step by step, we will analyze the given conditions and derive the required expression.

### Step 1: Understand the given conditions
We know that the sides \( a, b, c \) of triangle \( ABC \) are in Arithmetic Progression (A.P.). This means we can express the sides as:
- \( a = b - d \)
- \( b = b \)
- \( c = b + d \)

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