The Geckos That Trade Colors

A terrarium houses $45$ geckos: $13$ amber, $15$ teal, and $17$ crimson. Whenever two geckos of different colors meet, both instantly switch to the third color — an amber and a teal meeting both turn crimson, and so on. Meetings can be arranged in any order you like. Is there a sequence of meetings after which all $45$ geckos share a single color?