the multiplier $= \frac{1}{(1-MPC)}$
and
the multiplier $= \frac{1}{MPW} = \frac{1}{MPS+MPM+MPT}$.
Now since $MPC + MPS = 1$ it follow that $1-MPC = MPS$,
therefore the multiplier = $\frac{1}{(MPS+MPM+MPT)} = \frac{1}{MPS}$
and so $MPS = MPS + MPM + MPT$
from this, we can see that $MPM = -MPT$
Therefore, Marginal Propensity to Import = negative Marginal Propensity to Tax
I am unable to see what the flaw in the logic is or if there is something I am missing. Any explanation or help would be great.