Perform the required integrations:

v1 = (1/(2 π)) 
        Integrate[
          Sin[t  +  θ] Sin[s  +  θ], {θ, 0, 
            2 π}]

v2 = (1/(2 π)) 
        Integrate[
          Sin[ θ] Sin[t  +  θ], {θ, 0, 
            2 π}]

v3 = (1/(2 π)) 
        Integrate[
          Sin[ θ] Sin[s  +  θ], {θ, 0, 
            2 π}]

v4 = (1/(2 π)) 
        Integrate[Sin[ θ]^2, {θ, 0, 2 π}]

v1 - v2 - v3 + v4