One counterexample is theta = pi/4, because
sin(theta)*cos(theta) = sin(pi/4)*cos(pi/4) = sqrt(2)/2*sqrt(2)/2 = 1/2
while
cot(theta) = cot(pi/4) = cos(pi/4)/sin(pi/4) = (sqrt(2)/2)/(sqrt(2)/2) = 1
---------
After plugging in theta = pi/4, the equation
sin(theta)cos(theta) = cot(theta)
becomes
1/2 = 1
which is a false equation. This is enough to show we do not have an identity.
