I think the idiom is difficult because it's not a properly understood idiom for most people who speak English. It's a sailing term. When you're sailing into the wind, you criss-cross against it, changing the side of the ship the wind is coming across, so the ship ends up taking zig-zag path through the water. Changing the orientation of the ship so the wind comes across a different side is tacking. It's the opposite of jibing, which is changing which side the wind is coming across with the wind at your back.

Hopefully the context of it helps, taking "the opposite tack" is changing your orientation to reach towards the same goal on a different approach when you're getting off-course with your current approach.