What is the ruling if the times for Fajr and 'Isha prayers in the daily calendar differ significantly from the times announced by the muezzin, while the times for the other prayers are similar?

"Daily [calendars] and the timing of the adhan are merely means to clarify the entry of prayer times. If a Muslim finds these means contradictory or doubts them, he should refer to the clear cosmic signs explained by the Shari'ah to determine the prayer time, based on the Prophet's (peace and blessings be upon him) saying: 'The time for Dhuhr is when the sun declines and a man's shadow is like his height, as long as the time for Asr has not arrived. The time for Asr is as long as the sun has not turned yellow. The time for Maghrib is as long as the twilight has not disappeared. The time for Isha prayer is until the middle of the night. And the time for Fajr prayer is from the appearance of dawn as long as the sun has not risen.'"