If y = tan^(-1) ((1)/(x^(2) + x + 1)) + ...

If `y = tan^(-1) ((1)/(x^(2) + x + 1)) + tan^(-1) ((1)/( x^(2) + 3x + 3)) + tan^(-1) ((1)/( x^(2) + 5x + 7))+ tan^(-1) ((1)/( x^(2) +7x + 13)), x gt 0 ` and `((dy)/( dx))_(x=0)= ( - k )/( 1+ k)` then the value of k is

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