Given #tan(theta) = 1.437#, we can derive #tan^-1(1.437) = theta#. This is because #tan^-1(x)# is the inverse tangent of theta, that takes an value #x# (I used #x# so you wouldn't get confused) and returns an angle #theta# that the tangent of is #x#.
That's a bit confusing, let's list an example.
Say you have #tan(pi/4) = 1#,
then #tan^-1(1)# = #pi/4#.
"#x#" here is 1, and #theta# is #pi/4# radians.
In another light, this is just a question of substitution. We can reasonably get #theta = tan^-1(1.437)#, so by replacing the #theta# with the inverse expression...
#csc(theta) = csc(tan^-1(1.437))#
#sin(theta) = sin(tan^-1(1.437))#
We get an exact number that can be entered into a calculator for the irrational approximations shown in the answer above.
