"The weekly chart illustrates the gravity of this earnings release," Ross said. "Right now, the stock is precariously perched right at that key long-term 150-day moving average, which comes in right at $40," he said.
Coke shares "have been hanging around there a little bit too long," the technician said.
"I think on a bad number, which we just might get, you may get that break below $40, and that sets the stock up for further underperformance on both a relative and absolute basis."
David Seaburg, head of equity sales trading at Cowen, is similarly bearish.
"You may get a pop if they put a number up that's much better than the Street expects. But ultimately, long term, soda is dead, and that's their exposure," he said.
The latest confirmation of the downtrend came in March, when the trade publication Beverage Digest reported that Coca-Cola sales volume dipped 1.1 percent in 2014, and Diet Coke sales slid a painful 6.6 percent (thereby ceding second place in the U.S. soda rankings to Pepsi).
"There's probably a lot more downside risk than upside risk in that story. So again, I'd just stay far and clear away from this stock altogether," Seaburg said.
Of course, the earnings report may or may not mean a great deal for the stock.
"We do not see 1Q15 [earnings] as a major catalyst," wrote Nomura's research team in a recent note. The stronger dollar is likely to weigh on earnings, but by now analyst estimates are "fully discounting recent USD strength," the note said.