If `A=pi/5,` then find the value of `sum_(r=1)^8tan(r A)*tan((r+1)A)dot`

Explanation

To solve the problem, we need to find the value of the summation:

\[ S = \sum_{r=1}^{8} \tan(rA) \tan((r+1)A) \]

where \( A = \frac{\pi}{5} \).

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