For x in(0 (pi)/(2)) If (int(tan x sqrt(...

For `x in(0 (pi)/(2))` If `(int(tan x sqrt(sec x)(1+cos^(2)x))/(sqrt(cos x+sin^(2)x))dx=2sqrt(f(x)+1)+c) and f((pi)/(3))=(3)/(2)` then `f((pi)/(4)) =` ( where [.] denotes G.1.F)

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