Дано: cos(a) = 2/3

Найдем значение sin(a) с помощью теоремы Пифагора: sin^2(a) + cos^2(a) = 1
sin^2(a) + (2/3)^2 = 1
sin^2(a) + 4/9 = 1
sin^2(a) = 1 - 4/9
sin^2(a) = 5/9
sin(a) = sqrt(5/9) = sqrt(5)/3

Теперь найдем значение tg(a) и ctg(a):
tg(a) = sin(a)/cos(a) = (sqrt(5)/3) / (2/3) = sqrt(5)/2
ctg(a) = 1/tg(a) = 1 / (sqrt(5)/2) = 2/sqrt(5) = 2sqrt(5) / 5

Теперь найдем значение выражения sin(a) tg(a) ctg(a):
(sin(a)) (tg(a)) (ctg(a)) = (sqrt(5)/3) (sqrt(5)/2) (2sqrt(5) / 5) = (5/3) * (2/5) = 10 / 15 = 2 / 3

Ответ: sin(a) tg(a) ctg(a) = 2 / 3.