Depth Reduction of a Class of Witten Zeta Functions

We show that if $a,b,c,d,f$ are positive integers such that $a+b+c+d+f$ is even, then the Witten zeta value $\zeta_{\mathfrak{sl}(4)} (a,b,c,d,0,f)$ is expressible in terms of Witten zeta functions with fewer arguments.