Let \( m_1,m_2 \) be the slopes of two adjacent sides of a square of side \( a \) such that \( a^2+11a+3\!\left(m_1^2+m_2^2\right)=220 \). If one vertex of the square is \( \left(10(\cos\alpha-\sin\alpha),\,10(\sin\alpha+\cos\alpha)\right) \), where \( \alpha\in\!\left(0,\dfrac{\pi}{2}\right) \) and the equation of one diagonal is \( (\cos\alpha-\sin\alpha)x+(\sin\alpha+\cos\alpha)y=10 \), then \( 72(\sin^4\alpha+\cos^4\alpha)+a^2-3a+13 \) is equal to:
