The cause of this dieback would not be treatable with the spray pictured. It would be good to let the homeowner know that attempted treatment without first diagnosing the issue and confirming the cause of damage is not recommended, in part because you won't know what pesticide, if any, would be appropriate to use.

It's likely that the drought present for much of this past summer (which is still ongoing in most counties; see linked map) weakened the trees first, unless they were regularly being monitored for watering needs and periodically irrigated. Then, a secondary issue like wood-boring insects or a fungal canker disease invaded the vulnerable tissues. The dark trunk spots, oozing sap (called gummosis), and cracked bark suggest that either borers or a canker disease is present, though an overlap of both is also possible. Neither can be cured. With the extent of browning pictured, the affected plant(s) should be replaced, since they will not recover. We've seen many examples of 'Green Giant' arborvitae succumbing to drought (or secondary problems brought on by drought) this year. Too little soil moisture can also kill roots by itself, which will result in top dieback since the remaining roots cannot support all of the above-ground growth.

Replacements can be installed now if desired, though it's a bit late to be planting evergreens to reduce the risk of winter damage, so the alternative would be replanting in spring. Any time of year, new installations should be carefully monitored for watering needs, and the root balls loosened well if the roots were rootbound in the pot. (If burlapped, make sure all burlap and tying material or caging is removed before planting.) Stakes should not be needed, but if present, remove them after six months and make sure the material tied around the trunk is not constricting growth or damaging the bark, as that can cause top dieback as the plant grows.

Miri