trig help

1. 2 sin 2t − 3tan 2t = 0

2sin2t - 3sin2t / cos2t = 0

sin2t [ 2 - 3/cos2t]  = 0

Set each factor to 0

sin2t = 0    and this occurs at  n* pi/2     where n is an integer

For the second factor, we have

2 - 3/cos2t  = 0

2 - 3sec(2t)  = 0    

sec(2t)  = 2/3       and there is no solution to this 

Here's a graph [in degrees ]  .......https://www.desmos.com/calculator/x7dws0dxus

I assume that the second one is :

[6 cot t]^2  = 108

36cot^2 t  =  108       divide both sides by 36

cot^2 t  = 3       take the square root of both sides

cot t  =  ± sqrt (3)

For the first soluton, we have

cot t = sqrt(3)       this occurs at   pi/6 + n*pi    where n is an integer

For the second solution, we have

cot t = - sqrt(3)       this occurs at 5pi/6 + n*pi   where n is an integer 

Here's the graph [in degrees] :  https://www.desmos.com/calculator/hbl4cuxc3a

3. 16 tan t − 16 = 0    divide both sides by 16

tant - 1  = 0

tan t = 1       and this occurs at  pi/4  + npi     where  n is an integer