To find the values of sin 135, cos 210, tan 240, and cot 300, we can use the unit circle and trigonometric identities.

sin 135 = sin(90 + 45) = sin 90 cos 45 + cos 90 sin 45 = 1/sqrt(2) * 1/sqrt(2) + 0 = 1/sqrt(2) = sqrt(2)/2

cos 210 = cos(180 + 30) = cos 180 cos 30 - sin 180 sin 30 = -1 * sqrt(3)/2 - 0 = -sqrt(3)/2

tan 240 = tan(180 + 60) = tan 180 + tan 60 / 1 - tan 180 tan 60 = 0 + sqrt(3) / 1 - 0 sqrt(3) = sqrt(3)

cot 300 = cot(270 + 30) = cot 270 cot 30 - tan 270 tan 30 = 0 - 0 / 1 = 0

So the values are:
sin 135 = sqrt(2)/2
cos 210 = -sqrt(3)/2
tan 240 = sqrt(3)
cot 300 = 0