1 + sin 30° per cos 30° + sin 30° per 1 + sin 30°

= {(1+sin 30)² + (cos 30)²} / cos 30(1+sin 30)
= (1+2.sin30+sin²30+cos²30) / cos30(1+sin30)
= (1+2.sin30+1) / cos30(1+sin30)
= (2+2.sin30) / cos30(1+sin30)
= 2(1+sin30) / cos30(1+sin30)
= 2 / cos 30
= 2 sec 30
= 2(2/√3)
= 4/√3
= 4√3/3
= (4/3)√3