Let \( \vec{a},\vec{b} \) and \( \vec{c} \) be three vectors such that \( \vec{a}=\vec{b}\times(\vec{b}\times\vec{c}) \). If magnitudes of the vectors \( \vec{a},\vec{b} \) and \( \vec{c} \) are \( \sqrt{2},1 \) and \( 2 \) respectively and the angle between \( \vec{b} \) and \( \vec{c} \) is \( \theta \) \( (0<\theta<\dfrac{\pi}{2}) \), then the value of \( 1+\tan\theta \) is equal to :
