The most obvious connection between Tisha b’Av and parshat Vaetchanan—which is always read on the Shabbat following this saddest of days—lies in the opening lines of the parsha, where Moshe pleads to enter the land from which his beloved people would be exiled hundreds of years later.  

Our Torah encompasses all aspects of life: it regulates our existence from the day we are born until the day we die, and from the moment we awake until we retire at night. It is only after one has accepted the binding nature of the Law that one may begin to question the whys of the Law. While clearly some laws are more important than others, our attitude towards them all must be one of absolute obedience. "Be as meticulous in the light mitzvoth as in the heavy ones" (Avot 2:1).

"Shamor v’Zachor b’dibur echad". This phrase, sung every Friday night, notes the most famous difference between the recording of the aseret hadibrot in parshat Yitro, where we are commanded to “remember, zachor, the Shabbat” and Moshe's recounting of the events 40 years later, where we are commanded to “guard, shamor, the Shabbat”.  

“At that time I pleaded with G-d, saying, ‘O G-d, Lord…please let me cross the Jordan. Let me see the good land across the Jordan, the good mountain’”(Devarim 3:23-25). Moshe Rabbeinu had not yet given up his hope to enter the land of Israel. He pleaded, prayed, cajoled, negotiated, just so he could enter the Holy Land any which way, even as a foot soldier in Joshua's army. If only we had one iota of the depth of his feelings! Yet it was to no avail. 

Our Sages ordained that we should read parshat VaEtchanan on the Shabbat after Tisha B’Av. As they phrased it, “zumu v’tzlu, fast and pray”. On Tisha B’Av we fast, but we cannot pray. We can say words, but not words of prayer. “Though I cry to Him, He has blocked my prayer” (Eicha 3:8). Only after Tisha B’Av can we read of Moshe beseeching G-d to enter the Land of Israel.

Jews of faith, when faced with imminent death, have departed this world with the words of the shma on their lips. Perhaps the most famous example of this is the tragic death of Rabbi Akiva, one of the ten martyrs we read about on Tisha b'Av. As he was being tortured by the Romans, Rabbi Akiva gained a measure of comfort as he could now literally fulfil the mandate, "'and you shall love the Lord, your G-d, with all your soul', even when He takes your soul" (Brachot 54a).

Life is so unfair. While we believe that ultimately (and ultimately can take an eternity!) justice must and will prevail—to believe otherwise would be to deny the essence of Judaism—it is clear that life is full of injustices. Moshe Rabbeinu was the greatest person who ever lived. Yet he was denied his one wish, to be able to walk in and breathe the air of the land of Israel. Moshe continued pleading his case until G-d "angrily" told him, enough already! Your request is denied.

One of the fundamental beliefs of Judaism is that of reward and punishment. Keep the mitzvoth and get rewarded. Violate the laws of the Torah and be punished. This basic theme runs throughout much of the Torah – especially in sefer Devarim.