Complex Numbers

Let \(a,b\) be two real numbers such that \(ab < 0\). IF the complex number \(\frac{1+ai}{b+i}\) is of unit modulus and \(a+ib\) lies on the circle \(|z-1|=|2z|\), then a possible value of \(\frac{1+[a]}{4b}\), where \([t]\) is greatest integer function, is :