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This function grabs locks in different orders depending on the order
of the layers being drawn. But they are all released before being any
are grabbed again, and more than one lock grab only occurs on the
compositor thread.

R=pbos@chromium.org,earthdok
BUG=476529

Review URL: https://codereview.chromium.org/1081103009

Cr-Commit-Position: refs/heads/master@{#327304}