The correct choice would be “She believes in the latest technology” When referring to a particular technology, you would use the article the. When referring to technology in general, you would not use an article or the adjective latest in the sentence. This sentence is referring to a particular technology,

Articles like a, an, and the are one of the most difficult parts of English for non-native speakers of the language. You may not know which article to use, let alone whether to even use an article or not in front of a certain noun.

The refers to something specific. A and an is a general reference to the item or object. If the word in question is starts with a consonant sound, you use a, and if it starts with a vowel sound, then you use an.