Suppose that \(\frac{{\cos 2x}}{{\cos 2y}} = \frac{2}{3} % MathType!MTEF!2!1!+- % feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci % GGJbGaai4BaiaacohacaaIYaGaamiEaaqaaiGacogacaGGVbGaai4C % aiaaikdacaWG5baaaiabg2da9maalaaabaGaaGOmaaqaaiaaiodaaa % aaaa!41AF! \)

Find the value of \(\tan (x + y) \times \tan (x - y) % MathType!MTEF!2!1!+- % feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg % gacaGGUbGaaiikaiaadIhacqGHRaWkcaWG5bGaaiykaiabgEna0kGa % cshacaGGHbGaaiOBaiaacIcacaWG4bGaeyOeI0IaamyEaiaacMcaaa % a!4627! \)

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