Vector Algebra

\(\widehat u\) and \(\widehat v\) are two non-collinear unit vectors such that \(\left| {{{\widehat u + \widehat v} \over 2} + \widehat u \times \widehat v} \right| = 1\). Then the value of \(|\widehat u \times \widehat v|\) is equal to