There is no difference between "participate," and "take part in." For example, "I participate in sport," and "I take part in sport," are exactly the same in meaning. In this context, "to engage in," also has the same meaning. "To attend," has a different meaning. It means to go to something. "I attend football matches," has a very different meaning to "I participate in football matches." In the first case, you are watching the match, in the second you are playing in the match. Sometimes, if we are talking about a meeting, then the word 'attend," can have a similar meaning to the other terms: "I attend a meeting once a week." "I participate in a meeting once a week." "I take part in a meeting once a week." In these sentences the meanings are all similar. But the terms participate, take part in and engage in are more active terms than "to attend." Saying that you 'participate in a meeting,' implies that you had something to say and you were really involved in the meeting. If you merely attended it then you might have sat there in silence, or even fallen asleep during the meeting.