Let Z1 = (8 + i)sin theta + (7 + 4i)cos...

Let `Z_1 = (8 + i)sin theta + (7 + 4i)cos theta and Z_2 = (1 + 8i)sin theta + (4 + 7i)cos theta` are two complex numbers. If `Z_1* Z_2 = a + ib` where `a, b in R` then the largest value of `(a + b) AA theta in R`, is

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