I want this answer like in a ncert book

Sin^2a + (sinAcos(pie/3) + cosAsin(pie/3) )^2 + (sinACos(pie/3) - CosAsin(pie/3))^2
Sin^2a + 2Sin^2Acos^2(pie/3) + 2 Cos^2aSin^2(pie/3)
Sin^2a + 2 Sin^2A*1/4    + 2Cos^A*3/4
3/2 Sin^2A +  3/2 Cos^2 A
= 3/2 (sin^2a + cos^2a =1) = RHS