np complete – A query regarding Cubic 1 in 3 SAT Reduction

Given: An instance of 1-in-3 SAT problem.
Objective: Transform the problem to Cubic 1-in-3 SAT.

I have managed to reduce the problem such that, all variables have either exactly 1 or 3 occurance in the problem instance.

Since, the problem is almost Cubic 1-in-3 SAT the only thing left is to make sure each variable that occours once is repeated 3 times. I am struggling with that reduction. Of course the number of such varibles would be 3*x for some x.

Can someone please help with the reduction?