I have the EE RotK and heres how it goes...
Gandalf comes to Isengaurd for info and Saurman pulls out the Palantir and Wormtounge comes up and Theoden convinces him to come down and so Grima starts to, then Saurman smacks him, Grima falls pulls his dagger from the sheath stabs Saurman in the back 3 times Legolas shoots him with his bow and arrow, in the heart, Saurman falls onto his machinery, and so ends Saurman.
Hope this helps.