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By Global Public Square staff

You have all seen or heard or read about the grim situation in Syria – with thousands upon thousands of civilians dead. You might be less aware that the second most violent country in the world these days is Iraq. Yes, the country that we intervened in, with 180,000 troops at the peak, and hundreds of billions of dollars. Ten years later, it has levels of violence that would be described as a civil war anywhere else. More than 700 people died in a spate of bombings last month alone and the death toll, according to the United Nations, is over 3,000 in the last four months.

For many Americans, Iraq is a forgotten country. But recent events there provide an important set of lessons – not only for Iraq, but also for its Arab Spring neighbors, and for Syria in particular.

But let's go back to what sparked the current bout of violence. In April, Iraqi security forces killed more than forty people when they stormed a camp of protestors. The demonstrators were Sunni Muslims. Iraq's government, of course, is led by Shia Muslims. For years now, these Shias have gained power and used their majority to win elections and then brutally sideline the Sunnis. Remember, much of this is retribution: Saddam Hussein was a Sunni leader who brutally mistreated the majority Shias. The wheels of revenge keep turning.

Where did Washington fail? Some point to our withdrawal in 2011, when the White House failed to convince Baghdad it should retain a small presence of U.S. troops to train Iraqis and boost security. But even that would not have been more than a Band-Aid. Remember that when the Iraq war was at its worst, when sectarian violence killed thousands every month, we had more than 100,000 troops on the ground. Foreign troops cannot stop an internal civil war.

More from CNN: Are dark days returning to Iraq?

When the violence finally declined in Iraq, the real reason wasn't just coercion from American troops, but inclusion. General David Petraeus did wonders with a counterinsurgency campaign, but his chief contribution was to make peace with the Sunni tribes that had, so far, been battling the new Iraqi government. That effectively ended the insurgency. The Baghdad government promised, for its part, to treat the Sunnis as genuine partners and share power in every respect.

But within a few years, it became clear that these were false promises. Instead of reassuring other sects, the Shia-led government has dominated and intimidated. Its relations with the Kurds for example have become dysfunctional; with Sunnis they are now poisonous. Sunni discontent has bred conditions ripe for militant groups to flourish. Al Qaeda, which is Sunni-run, is fueling violence in Iraq. It is also working across the border in Syria, where it helps Sunni-rebels as they battle the Shia-Alawite regime of Bashar al-Assad.

Now, what can we do? Washington's failing is not a lack of military support so much, but a larger inability to broker a lasting political settlement among the key sects in Iraq. Of course, the biggest culprit here is Prime Minister Nuri al-Maliki, who has shown himself to be a Shia thug rather than a Mandela-like statesman.

In any revolution or upheaval, peace, stability and even democracy can only really emerge if the majority shares power with the minorities. Let's keep that in mind as we think about the rest of the Arab world, especially Syria. Getting rid of al-Assad and the Alawite sect that he represents would be a great step forward. But if the Sunni majority then chooses vengeance and reprisals, it will mean years of violence and instability, whether the U.S. is involved or not. Just take a look at Iraq.