Let the small square side length be 1 unit.
(a/sin30) = (1/sin15)
a = 1.93185165258 units.
a is the big square side length.
b² = 1.93185165258²+1-2*1.93185165258cos45
b = √(2) units.
b = 1.41421356237 units.
(1.93185165258/sinc) = (√(2)/sin45)
c = 75°
Therefore required angle is;
180-c
= 180-75
= 105°
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