As a special case, consider a (framed) $\theta$ graph, such that one zipping contains an unknotted component and another zipping is a split link, then the $\theta$ graph is isotopic to a planar one. This follows from a [theorem of Scharlemann][1], which states that if a band sum of knots is trivial, then the knots form a trivial link.   


  [1]: http://link.springer.com/article/10.1007%252FBF01388659