This Shell Rotella 15W40 already has "a shot of ZDDP".

"Our Rotella T4 15W-40 (CK-4) contains about 1200 ppm of zinc and 1100 of phosphous. These are the components of the ZDDP for anti-wear protection. Rotella T4 15W-40 (CK-4) is generally recommended for older flat tappet cam motors.""