Let M be the minimum value of f(theta)=(...

Let `M` be the minimum value of `f(theta)=(3cos^(2)theta+sin^(2)theta)(sec^(2)theta+3cos ec^(2)theta)` ,for permissible real values of `theta` and `P_(1),P_(2),...P_(n)(n>=1)` denotes the all real solutions of the equation `((x-1)(50-10x))/(x^(2)-5x)=x^(2)-8x+7` then `(sum_(i=1)^(n)P_(i))+M,` equals

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