By Emma Rumney and Isabel Woodford LONDON/MEXICO CITY (Reuters) – Diageo faces a battle to win back some investors’ trust following last month’s profit warning as the Johnnie Walker whisky and Tanqueray gin maker tries to revive its struggling Latin American division. Diageo warned last month that sales in Latin America and the Caribbean would fall by over 20% during the first half of its fiscal year, partly blaming a build-up of unsold stock in Mexico. That caused its shares to fall to near three-year lows. They are down 22% year to date and have been treading water since last month’s warning…