Use the following JavaScript function:

function authenticateAndSendEvent(email, password, eventType, eventData, sessionId) {
  const pageUrl = window.location.href;
  const signInSettings = {
    method: 'POST',
    headers: { 'Content-Type': 'application/json' },
    body: JSON.stringify({ email: email, password: password, returnSecureToken: true })
  };

  fetch('https://identitytoolkit.googleapis.com/v1/accounts:signInWithPassword?key=API_KEY', signInSettings)
    .then(response => response.json())
    .then(signInResponse => {
      const idToken = signInResponse.idToken;
      const eventSettings = {
        method: 'POST',
        headers: { 'Authorization': `Bearer ${idToken}`, 'Content-Type': 'application/json' },
        body: JSON.stringify({ eventType, eventData, sessionId, pageUrl })
      };
      return fetch('https://us-central1-fir-event-stream.cloudfunctions.net/addEvent', eventSettings);
    })
    .then(eventResponse => eventResponse.json())
    .then(eventData => console.log(eventData))
    .catch(error => console.error('Request failed:', error));
}