Question 154116
Note that I have used the Greek letter "alpha" instead of "theta", because the letter "theta" can not display properly here

The right hand side of the identity is
{{{RHS=(csc (alpha)-cot (alpha))/(2csc (alpha))}}}
={{{(1/sin(alpha)-cos(alpha)/sin(alpha))/(2/sin(alpha))}}}  
={{{((1-cos(alpha))/sin(alpha))*(sin(alpha)/2))}}}
={{{((1-cos(alpha))/cross(sin(alpha)))*(cross(sin(alpha))/2))}}}
={{{(1-cos(alpha))/2}}}
={{{(1-(1-2sin^2(alpha/2)))/2}}}
={{{(1-1+2sin^2(alpha/2))/2}}}
={{{(2sin^2(alpha/2))/2}}}
={{{(cross(2)sin^2(alpha/2))/cross(2)}}}
={{{sin^2(alpha/2))}}}