4/3 cot square 30 degrees + 3 sin square 60 degrees-2 cosec square 60 degrees -3/4 tan square 30 degrees =10/3

4/3 cot²30 + 3 sin²60 - 2 cosec²60 - 3/4 tan²30

Putting values of sin 60, cot 30, cosec 60, tan 30 we get

(4/3) (√3)² + 3 (√3/2)² - 2 (2/√3)² - (3/4) (1/√3)²

= (4/3) (3) + 3 (3/4) - 2 (4/3) - (3/4) (1/3)

= 4 + 9/4 - 8/3 - 1/4 = 4 + 9/4 - 1/4 - 8/3 (Rearranging)

= 4 + 8/4 - 8/3 = 4 + 2 - 8/3

= 6 - 8/3 = (18 - 8)/3

= 10/3